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Method for Modeling Transport Processes in Fluids

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The invention titled "Analytical Tools and Methods for Modeling Transport Processes in Fluids" US Patent No. 10467362 discloses a computer-implemented method for modeling fluid transport processes. Instead of modeling using an infinitesimal fluid element of a continuous medium, generally used in Computer Fluid Dynamics (CFD) simulations, the method approximates fluid flow in a fluid system as a model gas flow in a model gas system identical to the fluid system. The invention is not limited to modeling fluid in the form of gas. It can apply to any fluid in which property/information carriers have an arbitrary propagation component. rnThe invention is raised from an unexpected discovery that the property balance shall be maintained in each point of space occupied by chaotically moving particles carrying properties including mass, momentum, energy, or any other information property at any particular time (see FIG.13 of the specification). Later, in the Inventor's publications [1-4] supporting the patent invention, the Inventor named the discovered effect of the Ballistic Principle of the Property Balance in Space (BPPBS). rnThe BPPBS is based on recognizing that each particle composing the gas travels with a probability between any of two points in space occupied by the gas while following a ballistic trajectory governed by a law of motion in free space. Each ballistic particle is treated as a property carrier transporting one or more mass, momentum, and energy between the points of consecutive collisions. Each point in space occupied by the model gas is a sink accumulating property delivered by converging ballistic particles from the entire model gas system and a source dispersing property by diverging ballistic particles into the entire model gas system. All mentioned elements are incorporated in the independent claims 1, 6, 26, 29, and 30 and the supporting dependent claims. rnIt is worth noting that according to the BPPBS, each given point in space at a given time is a point of reality (present) or a pivot point of consuming the results of events from the gas space that occurred in the past and sending the result of consumption and balancing from the present into the future. The value of the property/information at the given point in space at the given time, which will be sent in the future, can be determined by solving the balance equations formulated using analytical tools according to the present invention [1, 2, 3]. rnHere, the Inventor admits the virtual nature of the balance described by the BPPBS. The value of property/information carried by a particle ejected from a given point in space at a given time seems to be not a result of preceding physical interactions by collisions of all available converging ballistic particles capable of targeting with a certain probability the given point in space at the given time (present time), but the result of the expectation of that value because of the cumulative effect from the surrounding space, in which each point of space complies with the BPPBS. rnThe BPPBS is validated by demonstrating that:rn1) The rate of collisions per unit area and the gas pressure exerted on the gas-solid interface of an ideal gas calculated by the patented method corroborates with the kinetic theory of ideal gases [1, 2] andrn2) The differential equations obtained by reducing from the formulated according to the patent integro-differential mass and momentum balance equations are identical to the Navier-Stokes equations [1, 2, 4]. rnThe above suggests that the patent's inventive concepts can be used to develop probabilistic prediction algorithms. Moreover, the accuracy of the long-time prediction may be improved significantly because the solver will operate on the exact solutions of the integro-differential balance equations. Also, the prediction accuracy of the system's dynamic evolution, especially in the most recent times following the initial time, may be enhanced by the disclosed method of considering a pre-established or known dynamic history of the gas system before the initial time. None of the existing techniques may offer this option. Therefore, building a solver according to the patent (Claims 29 and 30) is of great advantage to implement the tools to solve problems using methods from probability. rnThe most significant improvements for CFD modeling by the invention advance these applications and industries:rn 1. Efficient and accurate modeling of transport processes in rarefied gases according to the inventive approach benefits airspace industries, astrophysics, microelectronics and nanoelectronics processing, and plasma processing. rn2. Enhancement in time resolution of computations for unstable flows according to the inventive approach advances applications for turbulence, shockwave, and detonation analysis, which may boost supersonic aircraft and spacecraft development. rn3. Innovative quantitative interpretation of the aging factor according to the inventive method enhances applications for radiation and nuclear physics, physics of chemical reactions, and plasma physics processing. rn4. Finally, an improvement associated with the disclosed method of considering a pre-established or known dynamic history of the fluid system during a pre-initial period benefits any application by providing increased certainty and accuracy in predicting the fluid system evolution. rnI expect that the CFD software developed according to the patented invention will be in demand in various industries and especially benefit airspace industries, astrophysics, microelectronics and nanoelectronics processing, and plasma processing. rnrn[1] Kislov, N. (2020) Ballistic Principle of the Property Balance in Space and Its Application to Modeling of Fluid Dynamics Problems. Journal of Applied Mathematics and Physics, 8, 1081-1122. DOI: 10.4236/jamp.2020.86084.rn[2] Kislov, N. (2020) Novel Analytical Molecular Dynamics Technique for Solving Fluid Dynamics Problems, Chapter 1. In: Theory and Practice of Mathematics and Computer Science Vol. 5 1-41 DOI: Link N. (2021) Effect of Ballistic Bouncing of Gas Particles across a Microchannel on Rarefied Gas Flows. Journal of Applied Mathematics and Physics, 8, 779-808. DOI: 10.4236/jamp.2021.94054rn[4] Kislov, N. (2021) Discovery of New Terms Associated with the Navier-Stokes Momentum Balance Equation and Finding the Evidence of its Inapplicability to Govern Fluid Flow in the Infinite Space. Journal of Applied Mathematics and Physics, 20, 731-771. DOI: 10.4236/jamp.2022.103052 rnrn

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