JP-7857077-B2 - A computer system for simulating physical processes using lattice Boltzmann-based scalar transport, which enforces the Galilean invariance of scalar transport.

JP7857077B2JP 7857077 B2JP7857077 B2JP 7857077B2JP-7857077-B2

Inventors

プラディープゴパラクリシュナン
ラオヤンジャン
フードンチェン
アヴィナッシュジャマラマダカ

Assignees

ダッソーシステムズアメリカスコーポレイション

Dates

Publication Date: 20260512
Application Date: 20201029
Priority Date: 20200807

Claims (20)

A scalar solver of a computing system simulates the movement of scalar particles representing a scalar quantity in a fluid volume from a first voxel defined by a lattice structure read from a computer storage device and represented by a state vector , to a second voxel defined by the lattice structure and represented by a state vector , wherein the scalar particles are carried by flow particles in the fluid volume, and the movement of the scalar particles causes scalar collisions between the scalar particles, thereby resulting in the diffusion of the scalar quantity into the volume . The steps include: using a flow solver of the computing system to simulate the motion of flow particles representing the volume of a fluid using a flow grid velocity set, wherein the motion of the flow particles causes flow collisions between the flow particles; The steps include: using the scalar solver of the computing system to find the value of a non-equilibrium post-collision scalar distribution function based on a Hermitian polynomial of a specified order that represents the scalar collision ; The steps include: determining the value of a specified-order non-equilibrium post-collision flow distribution function representing the flow collision using the flow solver of the computing system; A computer execution method, including...
The method according to claim 1, wherein the scalar distribution function after the non-equilibrium collision is Galilean invariant.
The method according to claim 1, wherein the scalar distribution function after non-equilibrium collision is related to the relative velocity of the flow particles within the volume of the fluid.
The method according to claim 1, wherein the movement of the scalar particles causes collisions between the scalar particles, resulting in the diffusion of the scalar quantity into the entire volume.
The scalar lattice velocity set, the scalar quantity, and the non-equilibrium post-collision scalar distribution function are, respectively, the first scalar lattice velocity set, the first scalar quantity, and the first non-equilibrium post-collision scalar distribution function, and the method is A computer is used to simulate the motion of a second scalar particle representing a second different scalar quantity in the volume of a fluid, using a second different set of scalar lattice velocity, wherein the second scalar particle is carried by the flow particle in the volume of the fluid, and the motion of the second scalar particle causes a second scalar collision between the second scalar particles; and based on the motion of the second scalar particle, The method according to claim 1, further comprising the step of determining a value for a second distinct non-equilibrium post-collision scalar distribution function of a specified order that represents the second scalar collision.
The method according to claim 1, wherein the scalar distribution function after the non-equilibrium collision retains the non-equilibrium moment for the scalar quantity and eliminates the non-equilibrium moment for the scalar quantity of a higher order than the specified order.
The method according to claim 1, wherein the scalar lattice velocity set supports hydrodynamic motion up to a specified order of scalar particle velocity.
The method according to claim 7 , wherein the specified order is an exponential function value associated with the ratio of fluid velocity to lattice sound velocity, and the scalar lattice velocity set supports the exponential function value.
The method according to claim 7 , wherein the specified order is selected from zero, first, and second order.
A step of determining the relative particle velocity of a particle at a specific location in the volume of the fluid using the flow grid velocity set, wherein the relative particle velocity is the difference between the absolute velocity of the particle at the specific location measured under zero flow of the fluid in the volume and the average velocity of the particle at the specific location in the volume. The method according to claim 1 , further comprising the step of determining a specified order non-equilibrium post-collision distribution representing the collision of the particles based on the relative particle velocity.
The method according to claim 1, wherein, for a fluid flow in a macroscopic situation, the specified order is the first moment proportional to the gradient of the scalar quantity.
The method according to claim 1, wherein the scalar distribution function after the non-equilibrium collision is proportional to the sum of the scalar lattice velocity sets obtained by dividing the Hermitian polynomial by the factorial of the order multiple of the dimensionless velocity of the fluid.
The method according to claim 12 , wherein the scalar distribution function after non-equilibrium collision is related to the sum of weighting factors corresponding to the weighting coefficients of the particle distribution function.
One or more processors, A memory connected to one or more processors in an operable manner, A computer storage device, The scalar solver of the computing system simulates the movement of scalar particles representing a scalar quantity in a fluid volume from a first voxel , defined by a lattice structure read from the computer storage device and represented by a state vector , to a second voxel, defined by the lattice structure and represented by a state vector , wherein the scalar particles are carried by flow particles in the fluid volume, and the movement of the scalar particles causes scalar collisions between the scalar particles, thereby resulting in the diffusion of the scalar quantity into the volume . The flow solver of the computing system simulates the motion of flow particles representing the volume of a fluid using a flow grid velocity set, wherein the motion of the flow particles causes flow collisions between the flow particles. The scalar solver of the computing system obtains the value of a non-equilibrium post-collision scalar distribution function based on a Hermitian polynomial of a specified order representing the scalar collision , and The flow solver of the computing system obtains the value of a specified-order non-equilibrium post-collision flow distribution function representing the flow collision. A computer system comprising a computer storage device that stores instructions for causing one or more processors to perform the following actions.
The computer system according to claim 14 , wherein the scalar distribution function after the non-equilibrium collision is Galilean invariant.
The computer system according to claim 14 , wherein the non-equilibrium post-collision scalar distribution function is related to the relative velocity of the flow particles within the volume of the fluid.
The computer system according to claim 14 , wherein the movement of the scalar particles causes collisions between the scalar particles, resulting in the diffusion of the scalar amount into the entire volume.
The scalar lattice velocity set, the scalar quantity, and the non-equilibrium post-collision scalar distribution function are, respectively, the first scalar lattice velocity set, the first scalar quantity, and the first non-equilibrium post-collision scalar distribution function, and the computer system The computer system simulates the motion of a second scalar particle representing a second different scalar quantity in the volume of the fluid, using a second different set of scalar lattice velocity, wherein the second scalar particle is carried by the flow particle in the volume of the fluid, and the motion of the second scalar particle causes a second scalar collision between the second scalar particles, and based on the motion of the second scalar particle, The computer system according to claim 14 , further comprising instructions for determining a value for a second distinct non-equilibrium post-collision scalar distribution function of a specified order representing the second scalar collision.
A computer program product stored on a non-temporary computer-readable medium, The scalar solver of a computing system simulates the movement of scalar particles representing a scalar quantity in a fluid volume from a first voxel , defined by a lattice structure read from a computer storage device and represented by a state vector, to a second voxel, defined by the same lattice structure and represented by a state vector , wherein the scalar particles are carried by flow particles in the fluid volume, and the movement of the scalar particles causes scalar collisions between the scalar particles, thereby resulting in the diffusion of the scalar quantity into the volume . The flow solver of the computing system simulates the motion of flow particles representing the volume of the fluid using a flow grid velocity set, wherein the motion of the flow particles causes flow collisions between the flow particles. The scalar solver of the computing system obtains the value of a non-equilibrium post-collision scalar distribution function based on a Hermitian polynomial of a specified order that represents the scalar collision . The flow solver of the computing system obtains the value of a specified-order non-equilibrium post-collision flow distribution function representing the flow collision, A computer program product comprising instructions for causing a system having one or more processors and memory for storing programs to perform a certain action.
The computer program product according to claim 19 , wherein the scalar distribution function after the non-equilibrium collision is Galilean invariant.

Description

Priority Claim This application claims priority under Section 119 of the United States Patent Act to U.S. Provisional Patent Application No. 62/927,828, filed on 30 October 2019, entitled “Galilean Invariant Lattice Boltzmann Collision Formulation for Scala Transport in High Speed Flow Simulations,” the entire contents of which are incorporated herein by reference. This explanation concerns computer simulations of physical processes, such as physical fluid flow. Flows with high Reynolds numbers have been simulated by generating discretized solutions to the Navier-Stokes differential equations by performing high-precision floating-point operations at each of many discrete spatial locations on variables representing macroscopic physical quantities (e.g., density, temperature, flow velocity). Another approach involves replacing the differential equations with what is commonly known as a lattice gas (or cellular) automaton, where the macroscopic-level simulation obtained by solving the Navier-Stokes equations is replaced by a microscopic-level model that performs operations on particles moving between sites on a lattice. The Lattice Boltzmann Method (LBM) has been used for a wide range of industrial applications involving complex geometries. However, in some cases, LBM is often limited to low Mach number flows (or Mach flows), for example, in applications involving slow flows (less than approximately Mach number 0.3). Existing LBM approaches use finite-difference-based solvers to solve scalars such as energy or scalar concentration in multiple types of flows. These finite-difference-based solvers negate many of the advantages of LBM approaches, such as localized computation, high scalability, and grid-independent solutions. The techniques discussed below overcome many of the fundamental limitations of LBM for high-speed flows, thus enabling the use of LBM for simulations across a wide range of applications, including not only low-speed flows (e.g., Mach numbers less than 0.3) but also high-speed flows such as Mach numbers greater than 0.3, and supersonic flows (e.g., Mach numbers greater than 1.0, and hypersonic or at least multiples of Mach number). Instead of using a finite difference approach, the technique discussed below employs further distribution functions for scalars and a scalar solver . The use of a scalar solver preserves these advantages of LBM techniques that would otherwise be lost by using a finite difference-based solver . These distribution functions are strongly coupled to the flow distribution; that is, these functions are carried along the lattice direction by the flow particles. In one embodiment, a computer execution method includes, by a computing system, simulating the motion of scalar particles representing scalar quantities in a fluid volume using a scalar lattice velocity set, wherein the scalar particles are carried by flow particles in the fluid volume, and the motion of the scalar particles causes collisions between the scalar particles, and evaluating (determining the value of) a non-equilibrium post-collide scalar distribution function of a specified order that represents the scalar collisions. The following are some of the other features disclosed herein, within the scope of the embodiments described above. The scalar distribution function after a non-equilibrium collision is Galilean invariant. The scalar distribution function after a non-equilibrium collision is related to the relative velocity of flow particles within the fluid volume. The motion of scalar particles causes collisions between them, leading to the diffusion of scalar quantities into the entire volume. The method involves using a computing system to simulate the motion of flow particles representing the volume of a fluid using a flow grid velocity set, simulating that the motion of the flow particles causes collisions between the flow particles, and further comprising evaluating a specified order of non-equilibrium post-collision flow distribution function representing the flow collisions. The scalar lattice velocity set, scalar quantity, and non-equilibrium post-collision scalar distribution function are, respectively, the first scalar lattice velocity set, the first scalar quantity, and the first non-equilibrium post-collision scalar distribution function. The method further comprises simulating, using a computer, the motion of a second scalar particle representing a second different scalar quantity in a fluid volume, where the second scalar particle is carried by flow particles in the fluid volume, and the motion of the second scalar particle causes collisions between the second scalar particles; and evaluating, based on the motion of the second scalar particle, a second different non-equilibrium post-collision scalar distribution function of a specified order representing the second scalar collision. The non-equilibrium post-collision scalar distribution function preserves the non-equilibrium moment for sca