DETAILED ACTION
This action is in response to the amendments filed on Nov. 18th, 2025. A summary of this action:
Claims 1-3 and 5-6 have been presented for examination.
Claims 1-3, 5-6 are objected to because of informalities
Claims 1-4, 5-6 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea of both a mathematical concept and mental process without significantly more.
This action is Final
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Response to Arguments/Amendments
Regarding the § 112 Rejections and objections
Withdrawn in view of amendment. New objections below.
Regarding the § 101 Rejection
Maintained, updated as necessitated by amendment.
With respect to the remarks, at prong 1, regarding the establishing limitation, these are moot, as the rejection did not state that the establishing step was part of the abstract idea, but rather an additional element at prong 2 and step 2B.
Regarding the central velocity field/volume fraction distribution obtaining step, also moot – the rejection did not state these were mental, but rather math, and these remarks merely just make that more clear, i.e.: “Computing central velocity fields and volume-fraction distributions with a finite volume method is a computer-executed numerical solution of partial differential equations on mesh data structures.”
With respect to the defining step, the claim does not recite how this step is to be performed, let alone limit the claim expressly to what is disclosed, and its improper to import limitations into the claim which have no express basis in the claim. MPEP § 2111: “In re Prater, 415 F.2d 1393, 1404-05, 162 USPQ 541, 550-51 (CCPA 1969) (Claim 9 was directed to a process of analyzing data generated by mass spectrographic analysis of a gas. The process comprised selecting the data to be analyzed by subjecting the data to a mathematical manipulation. The examiner made rejections under 35 U.S.C. 101 and 35 U.S.C. 102. In the 35 U.S.C. 102 rejection, the examiner explained that the claim was anticipated by a mental process augmented by pencil and paper markings. The court agreed that the claim was not limited to using a machine to carry out the process since the claim did not explicitly set forth the machine. The court explained that "reading a claim in light of the specification, to thereby interpret limitations explicitly recited in the claim, is a quite different thing from ‘reading limitations of the specification into a claim,’ to thereby narrow the scope of the claim by implicitly adding disclosed limitations which have no express basis in the claim." The court found that applicant was advocating the latter, i.e., the impermissible importation of subject matter from the specification into the claim.).”
With respect to Contour IP Holding LLC v. GoPro, regarding the subject matter in claim 4 that has been incorporated into claim 1, the Examiner notes this was considered as further limiting the abstract idea itself – MPEP § 2106.05(I): “An inventive concept "cannot be furnished by the unpatentable law of nature (or natural phenomenon or abstract idea) itself." Genetic Techs. Ltd. v. Merial LLC, 818 F.3d 1369, 1376, 118 USPQ2d 1541, 1546 (Fed. Cir. 2016)” – furthermore, see the discussion of the focus of the claimed advance in the § 101 rejection, which is left unrebutted.
With respect to the § 102/103 remarks, MPEP § 2106.05(I): “As made clear by the courts, the "‘novelty’ of any element or steps in a process, or even of the process itself, is of no relevance in determining whether the subject matter of a claim falls within the § 101 categories of possibly patentable subject matter." Intellectual Ventures I v. Symantec Corp., 838 F.3d 1307, 1315, 120 USPQ2d 1353, 1358 (Fed. Cir. 2016) (quoting Diamond v. Diehr, 450 U.S. at 188–89, 209 USPQ at 9). See also Synopsys, Inc. v. Mentor Graphics Corp., 839 F.3d 1138, 1151, 120 USPQ2d 1473, 1483 (Fed. Cir. 2016) ("a claim for a new abstract idea is still an abstract idea. The search for a § 101 inventive concept is thus distinct from demonstrating § 102 novelty."). In addition, the search for an inventive concept is different from an obviousness analysis under 35 U.S.C. 103. See, e.g., BASCOM Global Internet v. AT&T Mobility LLC, 827 F.3d 1341, 1350, 119 USPQ2d 1236, 1242 (Fed. Cir. 2016) ("The inventive concept inquiry requires more than recognizing that each claim element, by itself, was known in the art. . . . [A]n inventive concept can be found in the non-conventional and non-generic arrangement of known, conventional pieces."). Specifically, lack of novelty under 35 U.S.C. 102 or obviousness under 35 U.S.C. 103 of a claimed invention does not necessarily indicate that additional elements are well-understood, routine, conventional elements” – i.e. Synopsys, Inc. v. Mentor Graphics Corp., 839 F.3d 1138, 1151, 120 USPQ2d 1473, 1483 (Fed. Cir. 2016) ("a new abstract idea is still an abstract idea") (emphasis in original) in 2106.04(I).
A better math concept is not eligible subject matter, without additional elements that either integrate the math concept into a practical application (e.g. Diamond v. Diehr as discussed in Mayo in MPEP § 2106.04(d)), or additional elements that amount to significantly more than the abstract idea itself, i.e. “Flook, 437 U.S. at 591-92, 198 USPQ2d at 198 ("the novelty of the mathematical algorithm is not a determining factor at all");” (MPEP § 2106.04(I)).
With respect to the remarks regarding prong 2, the Examiner respectfully disagrees for similar reasons as stated above, for, no matter how novel, groundbreaking, etc. an allegedly better math concept is, it is merely just a new abstract idea which is not eligible subject matter without being integrated into a practical application or reciting additional elements that amount to significantly more.
With respect to the 2B remarks, similar response as noted above.
As a further point of clarity as well, at the WURC consideration, the Examiner notes that switching between simulation modes for near the interface is WURC – e.g. see previously cited Ling, 2019, §§ 1.5-1.6, Fourtakas, 2018, § 1 including ¶¶ 1-4, and the other art of record cited at the WURC consideration, i.e. even if the discretizing limitations were considered as an additional elements as an insignificant computer implementation (MPEP § 2106.05(g)), than at 2B they do nothing more than invoke conventional technology in its ordinary capacity as a tool to perform the abstract idea.
Hence, as was noted in the previously stated reason why there was not art rejection, it was not the switching, but rather simply the “0.02” value recited in the claim.
Regarding the § 102/103 Rejection
Withdrawn in view of amendments. The reasons for withdrawing the rejection are noted on page 3 of the non-final rejection, Sept. 2025, and hereby incorporated by reference.
Claim Interpretation
The “thereby…” clause in claim 1 is interpreted as a desired result of the claimed invention, and thus given no weight. MPEP § 2111.04(I): “However, the court noted that a "‘whereby clause in a method claim is not given weight when it simply expresses the intended result of a process step positively recited.’" Id. (quoting Minton v. Nat’l Ass’n of Securities Dealers, Inc., 336 F.3d 1373, 1381, 67 USPQ2d 1614, 1620 (Fed. Cir. 2003)”
The Examiner further notes that this limitation appears to be intended for the § 101 remarks – MPEP § 2106.05(a): “That is, the claim must include the components or steps of the invention that provide the improvement described in the specification. However, the claim itself does not need to explicitly recite the improvement described in the specification (e.g., "thereby increasing the bandwidth of the channel").” – i.e. its recitation in the claim itself has no impact on the § 101 improvement consideration (also, see the rejection below and the prior rejection wherein the Examiner noted that this improvement was solely to the abstract idea itself).
As such, the Examiner suggests deleting this limitation, as it has no material effect on claim construction in view of the instant disclosure (¶ 7, ¶ 180, ¶ 196, etc.), and to ensure no ambiguity in the claim about whether or not this is a functional limitation merely claiming a desired result (MPEP § 2173.05(g)).
Claim Objections
Claims 1-3, 5-6 are objected to because of the following informalities:
The claims have numerous issues with antecedent basis. The Examiner suggests amending the claims such that the first recitation of each distinct element uses articles such as “a”/”an”, later recitations referring back to the same distinct element uses articles such as “the”/”said”, to use disambiguating modifiers (e.g., first, second, etc.) when there are multiple distinct elements with the same base term, and that the use of modifiers for each distinct element is kept consistent. Below is a non-exhaustive list of examples of these issues:
Claim 1 recites “the discrete dynamic model” and “the pseudo-fluid model” however these are not previously recited. Examiner suggests articles of “a”/”an” for the first recitation.
Claims 2-3 and 5-6 in the preambles recite the same preamble as claim 1, rather than referring back to it (e.g. “the whole atomization process of the…fuel”
Claim 2, “establishing a physical …” but this is referring back to the prior limitation. Examiner suggests “the”/”said”.
Claim 3 recites “for droplets” however this element was previously recited. Given the context of the claims and disclosure, the Examiner suggests amending to include the article “the”/”said”.
Claim 3, “viscous force…models” are previously recited
Claim 3: “discrete dynamic model….pseudo-fluid model” are previously recited
Claim 6: “a discrete element method” and “a smoothed discrete particle…” are now recited in claim 1 by the present amendments, but claim 6 does not refer back to the prior recitations.
Claim 6: “between DEM particles” – but see the “discretizing…” step for DEM now in claim 1 – in view of ¶ 167 and the following paragraphs, the Examiner suggests amending the claims to make it more clear the discretization for DEM introduces the DEM particles (¶ 167), and referring back to the recitation in claim 6.
Appropriate correction is required.
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.
Claims 1-4, 5-6 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea of both a mathematical concept and mental process without significantly more.
Step 1
Claim 1 is directed towards the statutory category of a process.
Step 2A – Prong 1
The claims recite an abstract idea of both a mental process and mathematical concept.
As a point of clarity, the focus of the alleged advance is on better math calculations. ¶ 7: “Therefore, the development of a simulation technology with the faster speed, higher efficiency and higher calculation accuracy is of great significance to evaluate the atomization performance of the aeroengine fuel nozzles.”
See MPEP § 2106.04(I): “The Supreme Court’s decisions make it clear that judicial exceptions need not be old or long-prevalent, and that even newly discovered or novel judicial exceptions are still exceptions. For example, the mathematical formula in Flook, the laws of nature in Mayo, and the isolated DNA in Myriad were all novel or newly discovered, but nonetheless were considered by the Supreme Court to be judicial exceptions because they were "‘basic tools of scientific and technological work’ that lie beyond the domain of patent protection." Myriad, 569 U.S. 576, 589, 106 USPQ2d at 1976, 1978 (noting that Myriad discovered the BRCA1 and BRCA1 genes and quoting Mayo, 566 U.S. 71, 101 USPQ2d at 1965); Flook, 437 U.S. at 591-92, 198 USPQ2d at 198 ("the novelty of the mathematical algorithm is not a determining factor at all"); Mayo, 566 U.S. 73-74, 78, 101 USPQ2d 1966, 1968 (noting that the claims embody the researcher's discoveries of laws of nature). The Supreme Court’s cited rationale for considering even "just discovered" judicial exceptions as exceptions stems from the concern that "without this exception, there would be considerable danger that the grant of patents would ‘tie up’ the use of such tools and thereby ‘inhibit future innovation premised upon them.’" Myriad, 569 U.S. at 589, 106 USPQ2d at 1978-79 (quoting Mayo, 566 U.S. at 86, 101 USPQ2d at 1971). See also Myriad, 569 U.S. at 591, 106 USPQ2d at 1979 ("Groundbreaking, innovative, or even brilliant discovery does not by itself satisfy the § 101 inquiry."). The Federal Circuit has also applied this principle, for example, when holding a concept of using advertising as an exchange or currency to be an abstract idea, despite the patentee’s arguments that the concept was "new". Ultramercial, Inc. v. Hulu, LLC, 772 F.3d 709, 714-15, 112 USPQ2d 1750, 1753-54 (Fed. Cir. 2014). Cf. Synopsys, Inc. v. Mentor Graphics Corp., 839 F.3d 1138, 1151, 120 USPQ2d 1473, 1483 (Fed. Cir. 2016) ("a new abstract idea is still an abstract idea") (emphasis in original).”
Also, see SAP v. InvestPic in MPEP § 2106.04(a)(2)(I).
An allegedly new math concept is still an abstract idea which is not eligible subject matter under 101, without additional elements that meaningfully integrate the math itself into a practical application (e.g. Diamond v. Diehr as discussed in Mayo as cited to in MPEP § 2106.04(d) first paragraph), or additional elements that amount to significantly more, e.g. MPEP § 2106.05(I): “An inventive concept "cannot be furnished by the unpatentable law of nature (or natural phenomenon or abstract idea) itself." Genetic Techs. Ltd. v. Merial LLC, 818 F.3d 1369, 1376, 118 USPQ2d 1541, 1546 (Fed. Cir. 2016). See also Alice Corp., 573 U.S. at 21-18, 110 USPQ2d at 1981 (citing Mayo, 566 U.S. at 78, 101 USPQ2d at 1968 (after determining that a claim is directed to a judicial exception, "we then ask, ‘[w]hat else is there in the claims before us?") (emphasis added)); RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) ("Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract"). Instead, an "inventive concept" is furnished by an element or combination of elements that is recited in the claim in addition to (beyond) the judicial exception, and is sufficient to ensure that the claim as a whole amounts to significantly more than the judicial exception itself. Alice Corp., 573 U.S. at 27-18, 110 USPQ2d at 1981 (citing Mayo, 566 U.S. at 72-73, 101 USPQ2d at 1966).”
See MPEP § 2106.04: “...In other claims, multiple abstract ideas, which may fall in the same or different groupings, or multiple laws of nature may be recited. In these cases, examiners should not parse the claim. For example, in a claim that includes a series of steps that recite mental steps as well as a mathematical calculation, an examiner should identify the claim as reciting both a mental process and a mathematical concept for Step 2A Prong One to make the analysis clear on the record.”
To clarify, see the USPTO 101 training examples, available at https://www.uspto.gov/patents/laws/examination-policy/subject-matter-eligibility.
The mathematical concept recited in claim 1 is:
establishing a physical fuel-gas-droplet multiphase flow model based on the 3D geometric model, the physical fuel-gas-droplet multiphase flow model comprising a physical fuel-gas two-phase flow model, a volume of fluid (VOF) functional model for tracking a gas-liquid two-phase interface as well as surface tension and viscous force constitutive models for the fuel; - math equations/relationships in textual form. ¶¶ 64-90: “For primary atomization of the fuel, an unsteady incompressible Navier-Stokes equation is used to establish the physical fuel-gas two-phase flow model; and both the surface tension model and the viscous force model are used as source terms and added to the Navier-Stokes equation... The discrete dynamic model for the droplets is established with the following equations… To track the gas-liquid two-phase interface, the VOF functional method is used to establish a physical interface tracking model. In a case where only the gas and liquid phases exist, the physical equation of the material is as follows: …After the model is established, physical parameters of each of the gas and the fuel in the atomization process are selected”
obtaining a central velocity field and a fluid volume fraction distribution of meshes with a finite volume method (FVM) based on the physical fuel-gas two-phase flow model, the VOF functional model for tracking the gas-liquid two-phase interface as well as the surface tension and viscous force constitutive models for the fuel; - math calculations/equations/relationships in textual form. See ¶¶ 56, then 92-119. The obtaining recitation, in view of the specification, is nothing more than a textual placeholder for calculating when given its BRI consistent with the disclosure for how the central velocity field and the like are obtained (i.e. by calculations).
transforming droplets less than a specified size in the atomization process into Lagrangian particle points; - math calculations/equations/relationships in textual form. See ¶¶ 126-131
and performing calculation on different volume fractions for the Lagrangian particles comprised in the meshes to obtain flow field data and droplet data on different time nodes – math calculations in textual form. ¶¶ 133-183
, wherein the performing calculation comprises: discretizing the discrete dynamic model for the droplets with a discrete element method (DEM) when a volume fraction for a Lagrangian particle in each of the meshes is less than or equal to 0.02: and discretizing the pseudo-fluid model for the droplets with a smoothed discrete particle hydrodynamics (SDPH) when the volume fraction for the Lagrangian particle in each of the meshes is greater than 0.02, thereby reducing calculation burden and improving calculation accuracy in simulating the atomization process. – part of the math calculations in textual form, wherein the discretizing is considered as part of the math calculations/relationships/equations in textual form. See ¶¶ 70-74, then see ¶¶ 92-95 noting the equations used for the discretization, also see ¶¶ 132-167 which further clarifies that discretization is math operations in mathematical calculations
Under the broadest reasonable interpretation, the claim recites a mathematical concept – the above limitations are steps in a mathematical concept such as mathematical relationships, mathematical formulas or equations, and mathematical calculations. If a claim, under its broadest reasonable interpretation, is directed towards a mathematical concept, then it falls within the Mathematical Concepts grouping of abstract ideas. In addition, as per MPEP § 2106.04(a)(2): “It is important to note that a mathematical concept need not be expressed in mathematical symbols, because "[w]ords used in a claim operating on data to solve a problem can serve the same purpose as a formula." In re Grams, 888 F.2d 835, 837 and n.1, 12 USPQ2d 1824, 1826 and n.1 (Fed. Cir. 1989). See, e.g., SAP America, Inc. v. InvestPic, LLC, 898 F.3d 1161, 1163, 127 USPQ2d 1597, 1599 (Fed. Cir. 2018)”
See MPEP § 2106.04(a)(2).
To clarify, see the USPTO 101 training examples, available at https://www.uspto.gov/patents/laws/examination-policy/subject-matter-eligibility.
The mental process recited in claim 1 is:
defining a gas and a liquid according to the central velocity field and the fluid volume fraction distribution; - a mental process, given the generality recited in this step, e.g. a person observing. See ¶¶ 56-57, as well as the disclosure portions cited above for the obtaining of the central velocity field, e.g. a person mentally observing the results of the central velocity calculation and fluid volume fraction, e.g. on the display of a computer or on a print-out, and mentally observing/judging which portions are gas and which portions are liquid, e.g. by observing the results of where the interface between the two are, e.g. by observing what cells in a mesh have liquid in them, and which ones do not have liquid
The discretizing steps noted above include a recitation of a mental process as well, specifically comparing two data values (the volume fraction value and 0.02) for the droplets, which is readily a mental judgement/evaluation/observation.
Under the broadest reasonable interpretation, these limitations are process steps that cover mental processes including an observation, evaluation, judgment or opinion that could be performed in the human mind or with the aid of physical aids but for the recitation of a generic computer component. If a claim, under its broadest reasonable interpretation, covers a mental process but for the recitation of generic computer components, then it falls within the "Mental Process" grouping of abstract ideas. A person would readily be able to perform this process either mentally or with the assistance of physical aids. See MPEP § 2106.04(a)(2).
To clarify, see the USPTO 101 training examples, available at https://www.uspto.gov/patents/laws/examination-policy/subject-matter-eligibility. In particular, with respect to the physical aids, see example # 45, analysis of claim 1 under step 2A prong 1, including: “Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited calculation, the use of such physical aid does not negate the mental nature of this limitation.”; also see example # 49, analysis of claim 1, under step 2A prong 1: “Moreover, the recited mathematical calculation is simple enough that it can be practically performed in the human mind. Even if most humans would use a physical aid, like a pen and paper or a calculator, to make such calculations, the use of a physical aid would not negate the mental nature of this limitation.”
As such, the claims recite an abstract idea of both a mental process and mathematical concept.
Step 2A, prong 2
The claimed invention does not recite any additional elements that integrate the judicial exception into a practical application. Refer to MPEP §2106.04(d).
The following limitations are merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea, as discussed in MPEP § 2106.05(f), including the “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more”:
establishing a three-dimensional (3D) geometric model for an aeroengine fuel atomizing nozzle and a spray flow field, the 3D geometric model being a mesh model; - part of the mere instructions to use a computer to do an abstract idea. ¶ 62: “The 3D geometric model for the nozzle and the spray flow field is established with commercial software Unigraphics (UG) and then imported to meshing software ANSYS-ICEM for regular meshing”
The following limitations are adding insignificant extra-solution activity to the judicial exception, as discussed in MPEP § 2106.05(g):
establishing a three-dimensional (3D) geometric model for an aeroengine fuel atomizing nozzle and a spray flow field, the 3D geometric model being a mesh model; - mere data gathering. ¶ 62: “The 3D geometric model for the nozzle and the spray flow field is established with commercial software Unigraphics (UG) and then imported to meshing software ANSYS-ICEM for regular meshing”
Should it be found that the discretizing steps are not part of the abstract idea, then the Examiner notes they would be considered an insignificant computer implementation (MPEP § 2106.05(g), as well as part of the mere instructions to invoke a computer and commonplace algorithms as a tool to perform the abstract idea.
A claim that integrates a judicial exception into a practical application will apply, rely on, or use the judicial exception in a manner that imposes a meaningful limit on the judicial exception, such that the claim is more than a drafting effort designed to monopolize the judicial exception. See MPEP § 2106.04(d).
E.g. MPEP § 2106(I): “Mayo, 566 U.S. at 80, 84, 101 USPQ2dat 1969, 1971 (noting that the Court in Diamond v. Diehr found “the overall process patent eligible because of the way the additional steps of the process integrated the equation into the process as a whole,”” – and see MPEP § 2106.05(e).
The claimed invention does not recite any additional elements that integrate the judicial exception into a practical application. Refer to MPEP §2106.04(d).
Step 2B
The claimed invention does not recite any additional elements/limitations that amount to significantly more.
The following limitations are merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea, as discussed in MPEP § 2106.05(f), including the “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more”:
establishing a three-dimensional (3D) geometric model for an aeroengine fuel atomizing nozzle and a spray flow field, the 3D geometric model being a mesh model; - part of the mere instructions to use a computer to do an abstract idea. ¶ 62: “The 3D geometric model for the nozzle and the spray flow field is established with commercial software Unigraphics (UG) and then imported to meshing software ANSYS-ICEM for regular meshing”
In claim 7, recitation such as the various modules
The following limitations are adding insignificant extra-solution activity to the judicial exception, as discussed in MPEP § 2106.05(g):
establishing a three-dimensional (3D) geometric model for an aeroengine fuel atomizing nozzle and a spray flow field, the 3D geometric model being a mesh model; - mere data gathering. ¶ 62: “The 3D geometric model for the nozzle and the spray flow field is established with commercial software Unigraphics (UG) and then imported to meshing software ANSYS-ICEM for regular meshing”
In addition, the above insignificant extra-solution activities are also considered as well-understood, routine, and conventional activities, as discussed in MPEP § 2106.05(d):
establishing a three-dimensional (3D) geometric model for an aeroengine fuel atomizing nozzle and a spray flow field, the 3D geometric model being a mesh model; - WURC in view of ¶ 62: “The 3D geometric model for the nozzle and the spray flow field is established with commercial software Unigraphics (UG) and then imported to meshing software ANSYS-ICEM for regular meshing” – see the evidence below as well
Should it be found that the discretizing steps are not part of the abstract idea, then the Examiner notes they would be considered an insignificant computer implementation (MPEP § 2106.05(g), as well as part of the mere instructions to invoke a computer and commonplace algorithms as a tool to perform the abstract idea, wherein they are WURC in view of the below evidence:
Ling, Y., et al. "A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability." Journal of Fluid Mechanics 859 (2019): 268-307. Abstract and §§ 1.5-1.6
Fourtakas, Georgios, et al. "An Eulerian–Lagrangian incompressible SPH formulation (ELI-SPH) connected with a sharp interface." Computer Methods in Applied Mechanics and Engineering 329 (2018): 532-552. Abstract and § 1
Kim, D., and P. Moin. "Numerical simulation of the breakup of a round liquid jet by a coaxial flow of gas with a subgrid Lagrangian breakup model." Annual Research Briefs, Center for Turbulence Research, Stanford University (2011): 15-30.§ 1 last three paragraphs
Ling, Yue, Stéphane Zaleski, and Ruben Scardovelli. "Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model." International Journal of Multiphase Flow 76 (2015): 122-143. Abstract and pages 123-124, then see page 125 col. 1, ¶¶ 1-3
Herrmann, Marcus. "A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure." Journal of computational physics 229.3 (2010): 745-759. Abstract, then see § 1 ¶¶ 2-4
Estivalèzes, Jean-Luc, and Davide Zuzio. "A multi-scale Eulerian-Lagrangian method for efficient DNS simulation of the assisted atomization of a planar liquid sheet." ICMF 2016. 2016. §§ 1-3
Gao, Jian, Mario F. Trujillo, and Suraj Deshpande. "Numerical simulation of hollow-cone sprays interacting with uniform crossflow for gasoline direct injection engines." SAE International Journal of Engines 4.2 (2011): 2207-2221. Abstract and the section “Numerical Approach” ¶¶ 1-3
Chéron, Victor, et al. "Hybrid treatment of small droplets in atomized jet." Congrés Francais de Mécanique. 2019. Abstract and introduction
Apte, S., Ehsan Shams, and Justin Finn. "A hybrid Lagrangian-Eulerian approach for simulation of bubble dynamics." (2009). Abstract and § 2
Chéron, Victor, et al. "From droplets to particles: Transformation criteria." ILASS-Europe 2019, 29th Conference on Liquid Atomization and Spray Systems. 2019. § 1
Pál, Botond, Dirk Roekaerts, and Barry Zandbergen. "Numerical investigation of atomisation using a hybrid Eulerian-Lagrangian solver." Progress in Computational Fluid Dynamics, an International Journal 21.6 (2021): 327-342. § 1 ¶¶ 1-4
Wenzel, Everett A., and Sean C. Garrick. "A Coupled Eulerian-Lagrangian Framework for the Modeling and Simulation of Turbulent Multiphase Flows." Modeling and Simulation of Turbulent Mixing and Reaction: For Power, Energy and Flight. Singapore: Springer Singapore, 2020. 227-250. Abstract and § 1 including ¶¶2-3, then see § 3 ¶ 1
Zuzio, Davide, et al. "A new efficient momentum preserving Level-Set/VOF method for high density and momentum ratio incompressible two-phase flows." Journal of Computational Physics 410 (2020): 109342. Abstract and § 1
Shinjo, Junji. "Recent advances in computational modeling of primary atomization of liquid fuel sprays." Energies 11.11 (2018): 2971. § 1 ¶¶ 3-4, then see § 2 incl. § 2.3; also § 3 ¶¶ 1-2
Palanti, Lorenzo, et al. "An implicit formulation to model the evaporation process in the Eulerian-Lagrangian Spray Atomization (ELSA) framework." Atomization and Sprays 29.12 (2019). § 1 ¶¶ 3-5
Sarthou, Arthur, Davide Zuzio, and Jean-luc Estivalezes. "Multiscale Eulerian-Lagrangian method for parallel simulation of atomization induced by air-blast planar injectors." 21st AIA A computational fluid dynamics conference. 2013. § 1 ¶¶ 2-3
Pereira, Gerald G., Paul W. Cleary, and Yoshihiro Serizawa. "Prediction of fluid flow through and jet formation from a high pressure nozzle using Smoothed Particle Hydrodynamics." Chemical Engineering Science 178 (2018): 12-26. Abstract and page 13 col. 2
The claimed invention is directed towards an abstract idea of both a mathematical concept and a mental process without significantly more.
Regarding the dependent claims
Claim 2 – mental judgements/opinions provided by a person, e.g. an engineer selecting and determining values of variables to use as inputs for the math calculations
Claim 3- adding more math equations/relationships to the math concept for similar reasons as discussed above
Claim 5 – math calculations in textual form
Claim 6 – math calculations in textual form
The claimed invention is directed towards an abstract idea of both a mathematical concept and a mental process without significantly more.
Conclusion
THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to DAVID A. HOPKINS whose telephone number is (571)272-0537. The examiner can normally be reached Monday to Friday, 10AM to 7 PM EST.
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If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Ryan Pitaro can be reached at (571) 272-4071. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
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/David A Hopkins/Primary Examiner, Art Unit 2188
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