Adaptive partitioning-based discrete unified gas kinetic scheme for flows in all flow regimes

To improve the efficiency of the discrete unified gas kinetic scheme(DUGKS)in capturing cross-scale flow physics,an adaptive partitioning-based discrete unified gas kinetic scheme(ADUGKS)is developed in this work.The ADUGKS is designed from the discrete characteristic solution to the Boltzmann-BGK equation,which contains the initial distribution function and the local equilibrium state.The initial distribution function contributes to the calculation of free streaming fluxes and the local equilibrium state contributes to the calculation of equilibrium fluxes.When the contribution of the initial distribution function is negative,the local flow field can be regarded as the continuous flow and the Navier-Stokes(N-S)equations can be used to obtain the solution directly.Otherwise,the discrete distribution functions should be updated by the Boltzmann equation to capture the rarefaction effect.Given this,in the ADUGKS,the computational domain is divided into the DUGKS cell and the N-S cell based on the contribu-tion of the initial distribution function to the calculation of free streaming fluxes.In the N-S cell,the local flow field is evolved by solving the N-S equations,while in the DUGKS cell,both the discrete velocity Boltzmann equation and the correspond-ing macroscopic governing equations are solved by a modified DUGKS.Since more and more cells turn into the N-S cell with the decrease of the Knudsen number,a significant acceleration can be achieved for the ADUGKS in the continuum flow regime as compared with the DUGKS.

THE ASYMPTOTIC PRESERVING UNIFIED GAS KINETIC SCHEME FOR GRAY RADIATIVE TRANSFER EQUATIONS ON DISTORTED QUADRILATERAL MESHES

In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme(DUGKS)for simulations of multiphase fluid flow,we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS.Due to the flux reconstruction procedure,additional terms that break the isotropic requirements of the pseudopotential model will be introduced.To eliminate the influences of nonisotropic terms,the expression of equilibrium distribution functions is reformulated in a moment-based form.With the isotropy-preserving parameter appropriately tuned,the nonisotropic effects can be properly canceled out.The fundamental capabilities are validated by the flat interface test and the quiescent droplet test.It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces.The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition.Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state.By directly incorporating the intermolecular interactions,the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors,which could help gain fresh insights into multiphase fluid flow.

A Gas Kinetic Scheme for the Simulation of Compressible Multicomponent Flows

In this paper,a gas kinetic scheme for the compressible multicomponent flows is presented by making use of two-species BGK model in[A.D.Kotelnikov and D.C.Montgomery,A Kinetic Method for Computing Inhomogeneous Fluid Behavior,J.Comput.Phys.134(1997)364-388].Different from the conventional BGK model,the collisions between different species are taken into consideration.Based on the Chapman-Enskog expansion,the corresponding macroscopic equations are derived from this two-species model.Because of the relaxation terms in the governing equations,the method of operator splitting is applied.In the hyperbolic part,the integral solutions of the BGK equations are used to construct the numerical fluxes at the cell interface in the framework of finite volume method.Numerical tests are presented in this paper to validate the current approach for the compressible multicomponent flows.The theoretical analysis on the spurious oscillations at the interface is also presented.

An implicit parallel UGKS solver for flows covering various regimes

This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

The Ellipsoidal Statistical model(ES-model)and the Shakhov model(S-model)were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heatflux.With the introduction of a new pa-rameter to combine the ES-model and S-model,a generalized kinetic model can be developed.This new model can give the correct Navier-Stokes equations in the con-tinuumflow regime.Through the adjustment of the new parameter,it provides abun-dant dynamic effect beyond the ES-model and S-model.Changing the free parameter,the physical performance of the new model has been tested numerically.The unified gas kinetic scheme(UGKS)is employed for the study of the new model.In transitionflow regime,many physical problems,i.e.,the shock structure and micro-flows,have been studied using the generalized model.With a careful choice of the free parameter,good results can be achieved for most test cases.Due to the property of the Boltz-mann collision integral,the new parameter in the generalized kinetic model cannot be fully determined.It depends on the specific problem.Generally speaking,the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model,while ES-model performs better in the cases where theflow is mostly driven by temperature gradient,such as a channelflow with large boundary temperature variation at high Knudsen number.