We present the formulation of a kinetic mapping scheme between the Direct Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is at the basis of the hybrid model used to couple the two methods in view of efficiently and accurately simulate isothermal flows characterized by variable rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we propose ensures to accurately couple DSMC and LBM at a larger Kn number than usually done in traditional hybrid DSMC-Navier-Stokes equation models. We show the main steps of the mapping algorithm and illustrate details of the implementation. Good agreement is found between the moments of the single particle distribution function as obtained from the mapping scheme and from independent LBM or DSMC simulations at the grid nodes where the coupling is imposed. We also show results on the application of the hybrid scheme based on a simpler mapping scheme for plane Poiseuille flow at finite Kn number. Potential gains in the computational efficiency assured by the application of the coupling scheme are estimated for the same flow.
Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli-trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging microchannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0$^{\circ}$ to 17$^{\circ}$ are described at different pressure ratios (1.5${\le}{\prod}{\le}$2.5) and Knudsen numbers (0.03${\le}$Kn${\le}$12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent microchannels and are compared with those of a …
Resolving Cryogenic and Hypersonic Rarefied Flows via Deep Learning-Accelerated Lennard-Jones DSMC
Ferdowsi University of Mashhad（马什哈德 Ferdowsi 大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Institute of Mechanics, Bulgarian Academy of Sciences（保加利亚科学院力学研究所）
In this paper, we employ the lattice Boltzmann method to solve the Boltzmann equation with the Shakhov model for the collision integral in the context of the 3D planar Couette flow. The half-range Gauss-Hermite quadrature is used to account for the wall-induced discontinuity in the distribution function. The lattice Boltzmann simulation results are compared with direct simulation Monte Carlo (DSMC) results for ${}^3{\rm He}$ and ${}^4{\rm He}$ atoms interacting via ab initio potentials, at various values of the rarefaction parameter $δ$, where the temperature of the plates varies from $1\ {\rm…
The present study employs the Direct Simulation Monte Carlo (DSMC) method, a widely used numerical method for studying non-continuum flows, to investigate the flow characteristics of a chemically reacting hypersonic flow over a backward-facing step. This work explores the effects of the Knudsen number on the behaviour of rarefied flow and compares the results with the non-reacting flow. The primary objective of the present thesis is to elucidate the variation of temperature in the flow domain with Knudsen number. The results of the study show that chemical reactions affect the temperature dist…
The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Kroo…
The importance of accurately capturing two-way coupled interactions between particles with complex shapes and rarefied gas flows is rapidly rising in different practical applications such as aerospace industry and semiconductor manufacturing. The transport of particles in these conditions is often modelled via an Euler-Lagrangian Point-Particles approach, where rarefaction effects are included through the phenomenological Cunningham corrections on the drag force experienced by the particles. In Point-Particles approaches, any explicit relation to the finite size of the particles, shape, orient…
The capability to simulate a two-way coupled interaction between a rarefied gas and an arbitrary-shaped colloidal particle is important for many practical applications, such as aerospace engineering, lung drug deliver and semiconductor manufacturing. By means of numerical simulations based on the Direct Simulation Monte Carlo (DSMC) method, we investigate the influence of the orientation of the particle and rarefaction on the drag and lift coefficients, in the case of prolate and oblate ellipsoidal particles immersed in a uniform ambient flow. This is done by modelling the solid particles usin…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important improvement is the scheme of temporal factors, allowing the use of different time step for different sorts of particles, thus reducing the complexity and/or resource usage in simulation of stationary problems with very different collisional cross-sections between components of a mixture. Other improvements include the similarity parameter for efficient estimation of…
The Bhatnagar-Gross-Krook (BGK) model as well as its extensions (ellipsoidal statistical BGK, Shakhov BGK, unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this end, different methods are investigated that allow efficient sampling of the Shakhov and the unified target distribution functions. As a consequence, particle simulations based on the Shakhov BGK and the unified BGK model are possible in an efficient way. Furthermore, different energy conservation schemes are tested for the BGK models. It is shown that the choi…
The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic relaxation models have been proposed and used in the past seventy years for the study of rarefied flow. In order to develop a multiscale method for the rarefied and continuum flow simulation, by adopting the integral solution of the kinetic model equation a DVM-type unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the cell…
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computational model, namely the nonlinear coupled constitutive relations(NCCR),was developed by R.S.Myong and applied successfully to one-dimensional shock wave structure and two-dimensional ra…
In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov and ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results obtained using these kinetic model equations with direct simulation Monte Carlo (DSMC) results for particles interacting via ab initio potentials. The analysis is restricted to channel flows between parallel plates and we consider three flow problems, namely: the heat transfer between stationary plates, the Couette flow and the heat transfer under shear. The …
We study a two phase flow with interactions of liquid and rarefied gas inside the gas phase. The gas phase is modeled by the BGK model of the Boltzmann equation. The liquid phase is modeled by the incompressible Navier-Stokes equations. In this paper we have excluded the heat transfer between two phases. The interface boundary conditions for the liquid and gas phases is presented. The BGK model is solved by a semi-Lagrangian scheme with a meshfree reconstruction since the droplet moves inside the gas phase and its interface deforms with respect to time and space. Therefore, the similar meshfre…
This paper presents recent investigation results on free molecular flows over a diffusely or specularly reflective ellipse, by using the gaskinetic theory. A virtual density distribution along the a diffusely reflective surface is introduced to aid the investigations. Many local surface properties are obtained, including surface slip velocity, coefficients for pressure, friction, and heat flux. Global coefficients for aerodynamic forces and moments, mass center-force center distances, are also obtained by integrating the local surface distributions. In the end, analytical expressions for the f…
For increasingly rarefied flowfields, the Navier-Stokes (NS) equations lose accuracy partially due to the single temperature approximation. To overcome this barrier, a continuum multi-temperature model based on the Bhatnagar-Gross-Krook (BGK) equation coupled with the Landau-Teller-Jeans relaxation model has been proposed for two-dimensional hypersonic non-equilibrium multi-temperature flow computation. In recent study, a two-stage fourth-order gas-kinetic scheme (GKS) has been developed for equilibrium flows, which achieves a fourth-order accuracy in space and time as well as high efficiency …
Accelerating Kinetic Fokker-Planck Simulations via a GPU-Native Deep Neural Network Surrogate: Application to Rarefied Internal and Hypersonic External Flows
Previously we presented a numerical model that predicts trajectories of lunar dust, soil, and gravel blown by the engine exhaust of a lunar lander. The model uses the gas density, velocity vector field, and temperature predicted by computational fluid dynamics (CFD) or Direct Simulation Monte Carlo (DSMC) simulations to compute the forces and accelerations acting on the regolith particles, one particle at a time (ignoring particle collisions until more advanced models are developed). Here we present significant improvements to the model, including the implementation of particle drag and lift f…
This paper is a continuation of our earlier work [Z.L. Guo {\it et al.}, Phys. Rev. E {\bf 88}, 033305 (2013)] where a multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, a discrete unified gas-kinetic scheme (DUGKS) for compressible flows with the consideration of heat transfer and shock discontinuity is developed based on the Shakhov model with an adjustable Prandtl number. The method is an explicit finite-volume scheme where the transport and collision processes are coupled in the evaluation of the flu…
This paper reports theoretical and numerical investigations on free molecular gas flows through micro-channels. Both diffusely and specularly reflective channel surfaces are considered. Gaskinetic methods are adopted to develop the analytical solutions for surface and flowfield properties. The crucial steps include constructing the velocity distribution functions (VDFs) for points at the plate surfaces and inside flowfield, and then completing the integration over the related velocity phases. For diffusely reflective surfaces, the VDFs are related to the densities and temperatures at the two e…
This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging iterative scheme. The memory reduction techniques in this method enable full three-dimensional (3D) solution of kinetic model equations in contemporary GPUs usually with a limited memory capacity that otherwise would need terabytes of memory. The GPU algorithm is validated against the DSMC simulation of the 3D lid-driven cavity flow and the supersonic rarefied …
In this paper, the unified gas-kinetic wave-particle (UGKWP) method is further developed for diatomic gas with the energy exchange between translational and rotational modes for flow study in all regimes. The multiscale transport mechanism in UGKWP is coming from the direct modeling in a discretized space, where the cell's Knudsen number, defined by the ratio of particle mean free path over the numerical cell size, determines the flow physics simulated by the wave particle formulation. The non-equilibrium distribution function in UGKWP is tracked by the discrete particle and analytical wave. T…
Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier-Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multicale transport. Due to the wave-particle decomposition, the dynamics in …
In this paper, a unified gas-kinetic scheme (UGKS) with simplified multi-scale numerical flux is proposed for the thermodynamic non-equilibrium flow simulation involving the excitation of molecular vibrational degrees of freedom in all flow regimes. The present UGKS keep the basic conservation laws of the macroscopic flow variables and the microscopic gas distribution function in a discretized space. In order to improve the efficiency of the UGKS, a simplify multi-scale numerical flux is directly constructed from the characteristic difference solution of the kinetic model equation. In addition…
