DETAILED ACTION
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Claims 1-18 are presented for examination.
This is non final.
Priority
Acknowledgment is made of applicant’s claim for foreign priority under 35 U.S.C. 119 (a)-(d). The certified copy has been filed in parent Application No. 2007110.6, filed on 14/05/2020.
Information Disclosure Statement
The Information disclosure statement submitted on 09/17/2024 was failed. See attached file for considered NPL documents. Only the copy of NPL that are provided are considered except, NPL by Knupp and Fries, since they are used against this application because they are qualified as a prior art under 35 USC 102(a)(1).
Specification
The disclosure is objected to because of the following informalities:
Reference 39, 40-42, 61-62, and 64 are not cited at the reference.
Para [0217], reference 29, year should be 2019 not 2009.
Appropriate correction is required.
Claim Rejections - 35 USC § 112
Claims 12 -13 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
The term “low ” in claim 12 is a relative term which renders the claim indefinite. The term “low ” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention.
For the rest of the claim low is interpreted as any value less than the other.
Claim 13 is also rejected, since it depends on claim 12.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claim 1- 18 are rejected under 35 U.S.C. 101 because the claim invention recites a
judicial exception, is directed to that judicial exception of an abstract idea, as it has not
been integrated into practical application and the claim further do not recite significantly
more than the judicial exception.
Step 1 ,Yes, the claims 1- 15 are directed to methods, which fall within the statutory category of process while claims 16 -18 are directed to a non- transitory computer readable medium and therefore is considered as a machine under
statutory category of invention.
Step 2A: Prong one: Yes, the claims recite abstract ideas
Regarding claim 1, the bolded claim limitations recite judicial exceptions( abstract ideas).
method of computational analysis of a physical system that is modelled by modelling equations representing relationships between physical properties of the physical system, the method comprising, (under its broadest interpretation , it is an abstract idea under mental process. A human can make observations, evaluations,
judgments, and opinions on the gathered information in order to find a relationship between the physical properties of the system by analyzing the modelling equation using a pen and paper. For example a person of ordinary skill in the art can analyze the relationship between size of volume and face area vector by drawing a graph. )
in respect of at least some of the nodes referred to as algebraic volume nodes, deriving face area vectors between algebraic volumes associated with each algebraic volume node and neighboring volumes in the mesh from solutions of discretized differential flux equations for each algebraic volume representing fluxes between the respective algebraic volume and each neighboring volume in the mesh;(under its broadest interpretation, this claim recites a mathematical concept of deriving a face area vector and a differential flux equation. According to the specification on para [0086], face area vector is calculated as the product of the areas of the pth face and neighboring nodes. The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. Therefor this claim limitation is abstract idea under mathematical concept.
discretizing an integral form of the modelling equations into volume equations in respect of volumes associated with respective nodes of the mesh, the volume equations in respect of each volume representing the relationship between the size of the volume, the face area vectors between the respective volume and neighboring volumes in the mesh, and fluxes across the face areas, (under its broadest interpretation this claim limitation recites a mathematical equation called volume equation with physical properties like size of volume and performs a mathematical concept called integration. The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. The Supreme Court has identified a number of concepts falling within this grouping as abstract ideas, (e.g., a relationship between reaction rate and temperature, which relationship can be expressed in the form of a formula called the Arrhenius equation, Diamond v. Diehr; 450 U.S. at 178 n. 2, 179 n.5, 191-92, 209 USPQ at 4-5 (1981);
solving the volume equations and deriving information on the physical properties of the physical system ( Under its broadest interpretation this claim limitation can be performed by a human mind with the aid of pen and paper. A person of ordinary skill in the art can solve the volume equation with pen and paper, and based on the derived information’s form the volume equation, a human can make observations, evaluations,
judgments, and opinions in order to drive information on the physical properties of the physical system.
Regarding claim 2
wherein the solutions of discretized differential flux equations are least squares solutions.( as it was listed on claim 1, this claim limitation also further defines a miasmatical concept called least squares solution)
Regarding claim 5
wherein the discretized differential flux equations are Taylor series expansions of the fluxes at midpoints between fluxes between the respective algebraic volume and each neighboring volume in the mesh (under its broadest interpretation, this claim limitation further defines a mathematical concept by using a Taylor series expansion (mathematical concept))
Regarding claim 6
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This claim recites a mathematical concept using matrix, transpose, inverse and it also recites a mathematical equation to find the face area vector. Under its broadest interpretation this claim is abstract idea under mathematical concept. A claim that recites a numerical formula or equation will be considered as falling within the "mathematical concepts" grouping ( e.g., a mathematical formula for hedging (claim 4), Bilski v. Kappos, 561 U.S. 593, 599, 95 USPQ2d 1001, 1004 (2010) (Fixed Bill Price = Fi + [(Ci + Ti + LDi) x (α + βE(Wi))]), MPEP 2106.04(a)(2))
Regarding claim 8
wherein the modelling equations are the Navier-Stokes equations, optionally including modifications for inviscid flow ( as it was listed above this claim also recites a mathematical equation called Navier-Stokes equations, so it is abstract idea under mathematical concept)
Step 2A : Prong 2, NO
The above judicially exceptions do not recite additional elements that integrate the
exceptions into a practical application of the exception because the claims do not have
additional elements of a combination of additional elements that apply, rely or use the
judicial exception in a manner that impose a meaningful limit on the judicial exception.
Claims recites gathering data which is insignificant extra solution activity. Adding
insignificant extra-solution activity to the judicial exception, e.g., mere data gathering in
conjunction with a law of nature or abstract idea such as a step of obtaining information
about credit card transactions so that the information can be analyzed by an abstract
mental process, as discussed in CyberSource v. Retail Decisions, Inc., 654 F.3d 1366,
1375, 99 USPQ2d 1690, 1694 (Fed. Cir. 2011) (see MPEP § 2106.05(g)).Claim 1 , generating a mesh of discrete nodes; (insignificant extra solution activity – data gathering)
In the claims 7 and 15 – 18, the claims recite additional elements of physical
system is a fluid system, common solver, computer program, A computer-readable storage medium and computer apparatus is used to merely implement the abstract idea on a computer and merely uses a computer device as a tool to perform the abstract idea is not integrating of abstract idea into practical application and to apply on a physical system (MPEP 2106(f). Generally linking the use of the judicial exception to a particular technological environment or field of use, e.g., a claim describing how the abstract idea of hedging could be used in the commodities and energy markets, as discussed in Bilski v. Kappos, 561 U.S. 593, 595, 95 USPQ2d 1001, 1010 (2010) or a claim limiting the use of a mathematical formula to the petrochemical and oil-refining fields, as discussed in Parker v. Flook, 437 U.S. 584, 588-90, 198 USPQ 193, 197-98 (1978) (MPEP § 2106.05(h)).
Dependent claims 3 - 4, 10-14 further narrows the abstract ideas by further defining the abstract concepts from the independent claim and they do not introduce further additional elements for consideration beyond those addressed above. The abstract ideas and insignificant extra activities are listed below for the above dependent claims.
As claim 3, discretized differential flux equations are weighted to enhance the numerical accuracy of the solutions( Under its broadest interpretation this claim limitation can be performed by a human mind with the aid of pen and paper, so this claim limitation is an abstract idea which fall under mental process. Some one of ordinary skill in the art can add some values like weight in to the differential flux equation and make analysis based on the value in order to make a judgment about the accuracy of the solution. Therefor this claim limitation is an abstract idea under mental process)
As of claim 4, wherein the sizes of the algebraic volumes are identical(Under its broadest interpretation this claim limitation can be performed by a human mind with the aid of pen and paper. A person of ordinary skill in the art can keep the algebraic volume the same by making observation , analysis and judgment on the value of algebraic volume. Therefor this claim limitation is an abstract idea under mental process).
As of Claim 10, in respect of nodes other than the algebraic volume nodes and referred to as finite volume nodes, deriving sizes of finite volumes associated with each finite volume node and face area vectors between the respective finite volume and neighboring volumes in the mesh from solutions of geometrical equations representing the geometry of the finite volumes (Under its broadest interpretation this claim limitation can be performed by a human mind with the aid of pen and paper. A person of ordinary skill in the art can extract the values of size of finite volume, face area vector for a geometric equation. According to the spect [106], “parameters are derived from solutions of geometrical equations representing the geometry of the finite volumes. This step may be performed in a conventional manner that is known for structured and unstructured meshes”. Therefore a person of ordinary skill can drive those parameters using a pen and paper from the geometric equation, so it is abstract idea under mental process.
the sizes and face area vectors represented in the volume equations in respect of the finite volume nodes are the sizes and face area vectors derived from the solutions of the geometrical equations( Insignificant extra activity – data defining)
As of Claim 11, further comprising selecting the at least some of the nodes as algebraic volume nodes and other nodes as finite volume nodes(( Insignificant extra activity – data defining)
As of claim 12, the method further comprises deriving at least one measure of quality of a finite volume associated with each node; (Under its broadest interpretation this claim limitation can be performed by a human mind with the aid of pen and paper. According to Spect [0032], a person of ordinary skill in the art can measure aspect ratio, skewness or make observation, analysis or judgment with physical aid. There for this claim limitation is abstract idea which fall under mental process.)
the step of selecting the at least some of the nodes comprises selecting nodes that are indicated by the at least one measure of quality to be of low quality as algebraic volume nodes and other nodes as finite volume nodes(this claim limitation also makes a judgment based on the measured value of quality, so a person of ordinary skill in the art can make observation, analysis or judgment by comparing measured value. A claim to collecting and comparing known information (claim 1), which are steps that can be practically performed in the human mind, Classen Immunotherapies, Inc. v. Biogen IDEC, 659 F.3d 1057, 1067, 100 USPQ2d 1492, 1500 (Fed. Cir. 2011); (MPEP 2106.04(a)(2)). There fore this claim limitation recites abstract idea which falls under mental process.
As of claim 13 measure of aspect ratio of the finite volume, a measure of skewness of the mesh in the locality of the node; a measure of smoothness of transitions in the size of finite volumes associated with neighboring nodes in the
locality of the node; and an orthogonal quality of the finite volume. ( Insignificant extra activity- data gathering)
As of claim 14, wherein the volume equations in respect of the algebraic volume nodes and the volume equations in respect of the finite volume nodes have a unified representation (Under its broadest interpretation this claim limitation recites a mental process. A person of ordinary skill in the art can use a common solver or common formula for both the algebraic node and finite node volume equation. So this claim limitation is abstract idea under mental process that some one in the art can use the same equation for two inputs using a pen and paper.)
Step 2B: No, The claims do not recite additional elements which are significantly more than the abstract idea. As outlined above the claims merely apply the abstract idea on a physical system and in order to perform the abstract idea, the claim recites a solver, and a computer as a tool. Merly using of a computer and applying abstract idea into a system without making improvement to the functionality of a computer and a physical system is not significantly more.
The dependent claims include the same abstract ideas as recited in the independent claim and merely incorporate additional details that narrow the scope of abstract ideas and fails to add significantly more than the claims.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1,4, 7-9 and 16-18 are rejected under 35 U.S.C. 103 as being unpatentable over Gang WANG, Yuewen JIANG, Zhengyin YE, “An Improved LU-SGS Implicit Scheme for High Reynolds Number Flow Computations on Hybrid Unstructured Mesh”, Chinese Journal of Aeronautics, Volume 25, Issue 1, 2012, in the view of H. Lomax T. H. Pulliam D. W. Zing “Fundamentals of Computational Fluid Dynamics” First Edition 2001. Corrected Second Printing 2003.
As of claim 1 Gang teaches a method of computational analysis of a physical system that is modelled by modelling equations representing relationships between physical properties of the physical system,( section 1 , “introduction”, Accompanied with the development of computational fluid dynamics (CFD), numerically solving the so-called Reynolds-averaged Navier-Stokes (RANS) equations has been widely used for viscous flow simulation in many industry fields)
generating a mesh of discrete nodes;( section 3.1, As shown in Fig. 1, a hybrid unstructured mesh for viscous flow simulation on NACA0012 airfoil is generated
with the method described in Ref. [16]. It consists of 200 wall boundary nodes, 7 991 computational field nodes and 11 552 mesh cells).
in respect of at least some of the nodes referred to as algebraic volume nodes, deriving face area vectors between algebraic volumes associated with each algebraic volume node and neighboring volumes in the mesh from solutions of discretized differential flux equations for each algebraic volume representing fluxes between the respective algebraic volume and each neighboring volume in the mesh( section 2.2, ” Spatial discretization’, by using the finite volume method for each grid cell
i, the spatial discretization of Eq. (1) can be expressed as
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where Ωi represents the volume of current grid cell i, N(i) the set of face neighbor cells of cell i, Sim the normal vector area of the face, the subscript im denotes the current face which is shared by cell i and cell m. In order to capture the discontinuity accurately and suppress numerical oscillations, a series of schemes has been developed for the evaluation of convective flux (Fc)im , for example the central scheme of Jamerson [13], the Roe scheme [14] and the AUSM type schemes [15]. However, all these schemes can be rewritten to the following unified form:
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)
Examiner Note: According to the spec [0082] “ Similarly, volumes whose parameters are derived from using the algebraic techniques described below will be referred to as "algebraic volumes" and the nodes associated therewith will be referred to as "algebraic volume nodes".” Therefore algebraic volume is interpreted as a calculated volume and as it shows above Gang teaches a volume of each grid cell, vector area of the face on the current and neighboring cell, and flux equation is also introduced as it cited above.
wherein the face area vectors represented in the volume equations in respect of the algebraic volume nodes are the face area vectors derived from the solutions of the discretized differential flux equations; (section 2.2, “Spatial discretization”
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where Ωi represents the volume of current grid cell i, N(i) the set of face neighbor cells of cell i, Sim the normal vector area of the face, the subscript im denotes the current face which is shared by cell i and cell m.)
solving the volume equations and deriving information on the physical properties of the physical system (section 2.1, “Governing equation”,
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where W = [ρ ρu ρv ρw ρE ρυ]T is the vector of conserved quantities with ρ, u, v, w, E and υ denoting the density, the Cartesian velocity components, the specific total energy and the working variable of S-A turbulence model, respectively. N represents the surface normal)
While Gang teaches having area vector for current and neighboring cell as it was listed above but Gang does not explicitly teach discretizing an integral form of the modelling equations into volume equations in respect of volumes associated with respective nodes of the mesh, the volume equations in respect of each volume representing the relationship between the size of the volume, the face area vectors between the respective volume and neighboring volumes in the mesh, and fluxes across the face areas.
However Lomax teaches discretizing an integral form of the modelling equations into volume equations in respect of volumes associated with respective nodes of the mesh, the volume equations in respect of each volume representing the relationship between the size of the volume, the face area vectors between the respective volume and neighboring volumes in the mesh, and fluxes across the face areas.( section 2.1, page 7-8, Conservation laws, such as the Euler and Navier-Stokes equations and our model equations, can be written in the following integral form:
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In this equation, Q is a vector containing the set of variables which are conserved, e.g. mass, momentum, and energy, per unit volume. The equation is a statement of the conservation of these quantities in a finite region of space with volume V(t) and surface area S(t) over a finite interval of time t2 - tl. In two dimensions, the region of space, or cell, is an area A(t) bounded by a closed contour C(t). The vector n is a unit vector normal to the surface pointing outward, F is a set of vectors, or tensor, containing the flux of Q per unit area per unit time, and P is the rate of production of Q per unit volume per unit time …)
Lomax is considered to be analogous to the claimed invention and Gang’s teaching, because they focus computational analysis of physical system. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied Lomax teaching of discretizing an integral form of the modelling equations like Euler and Navier Stokes equation on Gangs teaching of face area vector for current cel and neighboring cell with volume equation.
The motivation would have been using of modelling equation like Euler and Navier-Stokes and other model equations allows to develop a consistent framework of analysis for consistency, accuracy, stability, and convergence of computational analysis(Lomax, page 7).
As of claim 4, the combined model of Gang and Lomax teaches all the limitation of claim 1, and Gang also teaches the sizes of the algebraic volumes are identical (section 2.1- 2.2“ , the integral form of RANS equations enclosed with Spalart-Allmaras (S-A) turbulence model [11] for a control volume Ω with a surface element dS … and a fixed volume computational grid is used )
As of claim 7, the combined model of Gang and Lomax teaches all limitations of claim 1, and Gang also teaches wherein the physical system is a fluid system.(section 1, “introduction”, Accompanied with the development of computational fluid dynamics (CFD), numerically solving the so-called Reynolds-averaged Navier-Stokes (RANS) equations has been widely used for viscous flow simulation in many industry fields)
As of claim 8, the combined model of Gang and Lomax teaches all the limitations of claim 7,and Gang also teaches the modelling equations are the Navier-Stokes equations, optionally including modifications for inviscid flow.( section 1, “introduction”, Accompanied with the development of computational fluid dynamics (CFD), numerically solving the so-called Reynolds-averaged Navier-Stokes (RANS) equations has been widely used for viscous flow simulation in many industry fields)
As of claim 9, the combined model of Gang and Lomax teaches all the limitations of claim 1, and Gang also teaches the physical system has physical property that is conserved (section 2.1, “Governing equation”, the integral form of RANS equations enclosed with Spalart-Allmaras (S-A) turbulence model [11] for a control volume Ω with a surface element dS, where W = [ρ ρu ρv ρw ρE ρ]T is the vector of conserved quantities with ρ, u, v, w, E and υ denoting the density,…)
As of claim 16 Gang teaches a simulation system and it teaches A computer program capable of execution by a computer apparatus and configured, on execution, to cause the computer apparatus to perform a method according to claim 1 (Section1, “introduction”, In order to efficiently simulate high Reynolds number viscous flow with current limited computer hardware, highly stretched grids with large aspect ratios should be used to calculate the viscous effect in the boundary layer region.)
As of Claim 17, Gang teaches claim all of the limitations of claim 16, and as it was listed above it is obvious that a computer has a program and as of claim 18, Gang also listed CPU time comparation. ( section 2 -3). Examiner Note: As of claim 16-18, Gang performs simulation and it also compare CPU time of different modeling, so it is obvious that gang is using a computer with a program and storage as it is listed above to perform claim 1.
Claims 2-3 and 6 are rejected under 35 U.S.C. 103 as being unpatentable over Gang WANG, Yuewen JIANG, Zhengyin YE, “An Improved LU-SGS Implicit Scheme for High Reynolds Number Flow Computations on Hybrid Unstructured Mesh”, Chinese Journal of Aeronautics, Volume 25, Issue 1, 2012, in the view of H. Lomax T. H. Pulliam D. W. Zing “Fundamentals of Computational Fluid Dynamics” First Edition 2001. Corrected Second Printing 2003, further in the view of J. A White, H.Nishikawa, R.A Baurle “Weighted least-squares cell-average gradient construction methods for the VULCAN-CFD second-order accurate unstructured grid cell-centered finite-volume solver” - AIA A SciTech 2019
As of claim 2 , the combined model of Wang and Lomax teaches all the limitations of claim 1, but they do not explicitly teach wherein the solutions of discretized differential flux equations are least squares solutions.
While White teaches wherein the solutions of discretized differential flux equations are least squares solutions( section A, “Least-Squares Cell-Average Gradient Construction”, …the parameter used for the WLSQ gradients used in the inviscid flux reconstruction, 2 refers to the parameter used for the WLSQ gradients used in the construction of the cell face gradients for the viscous flux…)
White is considered as analogues to the combined model of Gang and Lomax, and the invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied White teaching of using weighted least square for inviscid flux reconstruction on the combined model of Gang and Lomax for discretize integration of the modelling equation.
The motivation would have been to accurately and robustly obtain Cell-average gradients on irregular, unstructured grids, that helps for accurately analyzing the flow fluid. (White, page 2)
As of claim 3, the combined model of Gang and Lomax teaches all the limitation of claim 1, but they do not explicitly teach wherein the discretized differential flux equations are weighted to enhance the numerical accuracy of the solutions.
While White teaches wherein the discretized differential flux equations are weighted to enhance the numerical accuracy of the solutions (section A, “Least-Squares Cell-Average Gradient Construction”, While no cell-average gradient method has been found to be accurate for all arbitrary polygons, with some caveats [14], the weighted linear least-squares method has been found to be a robust method when computing cell-average gradients [14-16] for node-centered and cell-centered 2nd-order finite-volume schemes).
White is considered as analogues to the combined model of Gang and Lomax, and the invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied White teaching of using weighted on flux reconstruction on the combined model of Gang and Lomax modelling equation to enhance accuracy.
The motivation would have been to accurately and robustly obtain Cell-average gradients on irregular, unstructured grids, that helps for accurately analyzing the flow fluid. (White, page 2)
As of claim 6, the combined model of Gang and Lomax teaches all the limitations of claim 1, but they do not explicitly teach wherein defining a matrix Am in respect of the m-th algebraic volume nodes by equation and the step of deriving face area vectors comprises solving a matrix [ ( Am T Am)-1 Am T] and deriving the face area vectors ΔSm,p in respect of the m-th algebraic volume node and its p-th neighboring nodes.
While White teaches defining a matrix Am in respect of the m-th algebraic volume nodes by the following equation
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(Section 1, page 2-3, For second-order finite-volume schemes, the gradients need to be at least first-order accurate on general unstructured grids; and thus, it is sufficient to fit a linear polynomial. Suppose we wish to compute the gradient of a solution variable q at a cell i, and have a set {gi} of N(≥ 3) nearby cells (i.e., a gradient stencil) available for fitting the linear polynomial
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and wj is the weight applied to the equation corresponding to the neighbor cell j.)
the step of deriving face area vectors comprises solving a matrix [(Am T Am)-1 AmT] and deriving the face area vectors ΔSm,p in respect of the m-th algebraic volume node and its p-th neighboring nodes as
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where ΔSm,p is the p-th element of the i-th row of the solved matrix [ ( Am T Am)-1 Am T]( Section A,
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Examiner Note: As white teaches a matrix of weight and coordinates above and calculated for x using inverse, Some one of ordinary skill can apply inverse and transpose on the matrix to find the equation. ( ATAx= bAT , x = ((ATA)-1AT) = ΔSm,p)
White is considered as analogues to the combined model of Gang and Lomax, and the invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied White teaching of using a matrix of weighted least square on a coordinate system to compute face area vector using simple mathematical calculation on the combined model.
The motivation would have been to accurately and robustly obtain Cell-average gradients on irregular, unstructured grids, that helps for accurately analyzing the flow fluid. (White, page 2)
Claim 5 is rejected under 35 U.S.C. 103 as being unpatentable over Gang WANG, Yuewen JIANG, Zhengyin YE, “An Improved LU-SGS Implicit Scheme for High Reynolds Number Flow Computations on Hybrid Unstructured Mesh”, Chinese Journal of Aeronautics, Volume 25, Issue 1, 2012, in the view of H. Lomax T. H. Pulliam D. W. Zing “Fundamentals of Computational Fluid Dynamics” First Edition 2001. Corrected Second Printing 2003, further in the view of , A. Christlieb, X. Feng, Y. Jiang and Q. Tang, "A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes," 2018 IEEE International Conference on Plasma Science (ICOPS), Denver, CO, USA, 2018
As of claim 5, the combined model of Gang and Lomax teaches all the limitation of claim 1, but they do not explicitly teach the discretized differential flux equations are Taylor series expansions of the fluxes at midpoints between fluxes between the respective algebraic volume and each neighboring volume in the mesh.
While Christleb teaches the discretized differential flux equations are Taylor series expansions of the fluxes at midpoints between fluxes between the respective algebraic volume and each neighboring volume in the mesh ( Section 3.1,
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Christleb is considered as analogues to the combined model of Gang and Lomax, and the invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied Christleb Taylor series expansion of flux equation and .using a numerical approximation to a point on algebraic and finite volumes as it taught on the combined mode.
The motivation would be to compute a high-order numerical flux by a Taylor expansion in space, with the lowest-order term solved from a Riemann solver and the higher order terms constructed from physical fluxes by limited central differences. ( Christleb, Abstract).
Claims 10 and 11 are rejected under 35 U.S.C. 103 as being unpatentable over Gang WANG, Yuewen JIANG, Zhengyin YE, “An Improved LU-SGS Implicit Scheme for High Reynolds Number Flow Computations on Hybrid Unstructured Mesh”, Chinese Journal of Aeronautics, Volume 25, Issue 1, 2012, in the view of H. Lomax T. H. Pulliam D. W. Zing “Fundamentals of Computational Fluid Dynamics” First Edition 2001. Corrected Second Printing 2003, further in the view of Jai Manik, Amaresh Dalal, Ganesh Natarajan, “A generic algorithm for three-dimensional multiphase flows on unstructured meshes”, International Journal of Multiphase Flow, Volume 106, 2018,
As of claim 10, the combined model of Gang and Lomax teach all the limitations of claim 1, but they do not explicitly teach, in respect of nodes other than the algebraic volume nodes and referred to as finite volume nodes, deriving sizes of finite volumes associated with each finite volume node and face area vectors between the respective finite volume and neighboring volumes in the mesh from solutions of geometrical equations representing the geometry of the finite volumes, and the sizes and face area vectors represented in the volume equations in respect of the finite volume nodes are the sizes and face area vectors derived from the solutions of the geometrical equations.
While Jai teaches in respect of nodes other than the algebraic volume nodes and referred to as finite volume nodes, deriving sizes of finite volumes associated with each finite volume node and face area vectors between the respective finite volume and neighboring volumes in the mesh from solutions of geometrical equations representing the geometry of the finite volumes ( section 3.1.2, “Diffusive flux treatment”, Using Gauss divergence theorem, the diffusive fluxes for variable φ (φ= φ/ρ are discretized in the following manner.
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where Sf is the face area vector with a magnitude of Af and its direction is given by unit vector n f . For non-orthogonal grids, the line joining adjacent cell centers is not aligned with the sur- face normal, thus giving rise to the non-orthogonal component of diffusive fluxes. To understand it, let us consider a geometrical arrangement as shown in Fig. 1 , where a face “abc” is shared by two neighboring tetrahedral cells with centers marked as P and N. The face unit normal is represented by ˆ n f . Projecting the cell centers over the surface normal will result in two more points P’ and N’)
the sizes and face area vectors represented in the volume equations in respect of the finite volume nodes are the sizes and face area vectors derived from the solutions of the geometrical equations( section 3.1.2, “Diffusive flux treatment”, …the face unit normal is represented by nf . Projecting the cell centers over the surface normal will result in two more points P’ and N’ . Now, we can write
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where Δn is the distance between points P’ and N’. Using Taylor series expansion for N’ and P’ and neglecting higher order terms, Eq. (11) can be written as
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Jai is considered as analogues to the combined model of Gang and Lomax, and the invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied Jai finite volume node associated with size and face area vector using geometrical equation and based on those equation someone in the art can find the size( as n) and face area vector using equations as Gang and Lomax teched above.
The motivation would have been to robust algorithm for multiphase flow simulations on unstructured meshes by considering physical properties like mass, and momentum with in a volume of fluid framework on orthogonal and non-orthogonal unstructured meshes (Jai, Introduction).
As of Claim 11, the combined model of Gang, Lomax and Jai teach all the limitations of claim 10, and Jai also teaches selecting the at least some of the nodes as algebraic volume nodes(section 5.3, In the present algebraic VOF approach, we choose to initialize the droplet in such a manner that it does not define the interface explicitly) and other nodes as finite volume nodes ( section 3.1, Following the work of Dalal et al. (2008) , we employ finite volume method to discretize the governing equations. The computational domain is subdivided into a large number of cells (control volumes).), as it is listed above Jai teaches both finite volume and algebraic volume of fluid.
Claims 12 and 13 are rejected under 35 U.S.C. 103 as being unpatentable over Gang WANG, Yuewen JIANG, Zhengyin YE, “An Improved LU-SGS Implicit Scheme for High Reynolds Number Flow Computations on Hybrid Unstructured Mesh”, Chinese Journal of Aeronautics, Volume 25, Issue 1, 2012, in the view of H. Lomax T. H. Pulliam D. W. Zing “Fundamentals of Computational Fluid Dynamics” First Edition 2001. Corrected Second Printing 2003, in the view of Jai Manik, Amaresh Dalal, Ganesh Natarajan, “A generic algorithm for three-dimensional multiphase flows on unstructured meshes”, International Journal of Multiphase Flow, Volume 106, 2018, in the view of Knupp P. M. Algebraic Mesh Quality Metrics, SIAM Journal on Scientific Computing, Vol. 23 (2001): 193-218 further in the view of Nathan J. Quinlan, Libor Lobovský, Ruairi M. Nestor, ”Development of the meshless finite volume particle method with exact and efficient calculation of interparticle area”, Computer Physics Communications, Volume 185, Issue 6, 2014,
As of claim 12, the combined model of Gang, Lomax and Jai teaches all the limitations of claim 11, but they do not explicitly teach the method further comprises deriving at least one measure of quality of a finite volume associated with each node; and the step of selecting the at least some of the nodes comprises selecting nodes that are indicated by the at least one measure of quality to be of low quality as algebraic volume
While Knupp teaches deriving at least one measure of quality of a finite volume associated with each node(section 2, “Preliminary observation”, An element quality metric is a scalar function of node positions that measures some geometric property of the element. If a three-dimensional element has K nodes with coordinates Xk E R3 , k = 0, 1, ... , K - 1, then we denote a mesh quality metric by f | R3K -> R. )
Knupp is considered as analogues to the combined model of Gang, Lomax and Jai , and the invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied Knupp quality measurement metric on the combined model of finite volume nodes.
The motivation would have been to improve the initial mesh quality of the finite nodes of the combined model by mesh improvement techniques such as smoothing, optimization, and edge swapping depend heavily on the use of quality metrics( Knupp, Introduction).
While the combined model of Gang, Lomax, Jai and Knupp do not explicitly teach
the step of selecting the at least some of the nodes comprises selecting nodes that are indicated by the at least one measure of quality to be of low quality as algebraic volume nodes and other nodes as finite volume nodes.
However Nathan teaches the step of selecting the at least some of the nodes comprises selecting nodes that are indicated by the at least one measure of quality to be of low quality as algebraic volume nodes and other nodes as finite volume nodes.( page 1561- 1562, the interface computed using VoF with mesh cell size ∆x/H = 1/600 (black curve) and the Finite Volume Particle Method (FVPM) is a meshless method,
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compared with an incompressible fluid model (VoF). At coarser resolution, FVPM displays less sensitivity than VoF to ∆x, with approximately half the range of kinetic energy for all cases but ∆x/H = 1/40.)
Examiner Note: according to the Spect on [0031], “selection of selection of nodes as finite volume nodes or algebraic nodes may be based on other criteria, for example based on distance from a moving object or on user input”, so as it showed on Fig. 16, Total kinetic energy can be used as a measurement.
Nathan is considered as analogues to the combined model of Gang, Lomax, Jali and Knupp, and the claim invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied Nathan comparation of total kinetic energy in order to differentiate the algebraic and finite volume nodes as it taught by the combined mode.
The motivation would have been by comparing volume of fluid method and finite volume particle method on the range of kinetic energy in order to select the accurate volume node to robust the combined model (Nathan, page 1562).
As of claim 13, the combined model of Gang, Lomax, Jai, Knupp and Nathan teach all the limitations of claim 12, and Knupp also teaches the at least one measure of quality includes one or more of the size of the finite volume; a measure of aspect ratio of the finite volume; a measure of skewness of the mesh in the locality of the node; a measure of smoothness of transitions in the size of finite volumes associated with neighboring nodes in the locality of the node; and an orthogonal quality of the finite volume(Introduction, volume, aspect ratio, skew, angles, stretching, and orientation are common geometric quality metrics)
Claims 14 and 15 are rejected under 35 U.S.C. 103 as being unpatentable over Gang WANG, Yuewen JIANG, Zhengyin YE, “An Improved LU-SGS Implicit Scheme for High Reynolds Number Flow Computations on Hybrid Unstructured Mesh”, Chinese Journal of Aeronautics, Volume 25, Issue 1, 2012, in the view of H. Lomax T. H. Pulliam D. W. Zing “Fundamentals of Computational Fluid Dynamics” First Edition 2001. Corrected Second Printing 2003, in the view of Jai Manik, Amaresh Dalal, Ganesh Natarajan, “A generic algorithm for three-dimensional multiphase flows on unstructured meshes”, International Journal of Multiphase Flow, Volume 106, 2018, further in the view of P. Fries, H. G. Matthies, A stabilized and coupled meshfree/mesh based method for the incompressible Navier-Stokes equations-part I: Stabilization, ComUS 2023/0185994 Al puter Methods in Applied Mechanics and Engineering, Vol. 195 (2006): 6205-6224.
As of claim 14, the combined model of Gang, Lomax and Jai teach all the limitations of claim 10, but they do not explicitly teach the volume equations in respect of the algebraic volume nodes and the volume equations in respect of the finite volume nodes have a unified representation.
While Fries teaches the volume equations in respect of the algebraic volume nodes and the volume equations in respect of the finite volume nodes have a unified representation.( Section 4.1, In [39], Gunther applies
SUPG stabilization to the compressible Navier–Stokes equations. It is not surprising that SUPG and GLS stabilizations work successfully for mesh based and meshfree methods as well, because close similarities in the theoretical analysis can be shown, see e.g. [46,47]. Therefore, one may expect that the theoretical foundation of SUPG and GLS accomplished for the mesh-based FEM applies analogously to meshfree methods.)
Fries is considered as analogues to the combined model of Gang, Lomax and Jali, and the claim invention, because they focus on computational analysis. Therefore, it would be obvious to one of the ordinary skills in the art before the effective filling date to have applied Fries teaching of analogous numerical stabilization method for both mesh based and meshfree methods on the combined model of algebraic and finite volume to have a unified volume representation.
The motivation would have been to create accurate and robust simulation by able to use Eulerian meshfree methods in stabilized Galerkin settings, totally analogously to mesh based standard FEM, opens the door to couple both methods for the solution of the incompressible Navier–Stokes equations (Fries, Conclusion)
As of claim 15, the combined model of Gang, Lomax, Jai and Fries teach all the limitations of claim 14, and Fries also teaches the step of solving the volume equations uses a common solver for the algebraic volume nodes and the finite volume nodes(Abstract , stabilization is needed in order to enable equal order interpolations of the incompressible Navier–Stokes equations. Standard stabilization techniques, developed in a mesh-based context, are extended to meshfree methods. It is found that the same structure of the stabilization schemes may be used. )
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Shaw; Gareth (US 20060129366 A1 Date Published 2006-06-15), this invention also teaches a finite volume method using a physical properties and integration of flux over a geometrical volume.
F. Moukalled • L. Mangani M. Darwish The Finite Volume Method in Computational Fluid Dynamics An Advanced Introduction with OpenFOAM® and Matlab®, 2016, this textbook also teaches a finite volume method on computational fluid using discretization of flux integration over element faces.
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/A.A.T./Examiner, Art Unit 2188
/RYAN F PITARO/Supervisory Patent Examiner, Art Unit 2188