A generalized sphere function-based gas kinetic scheme for simulation of compressible viscous flows

In this paper, a generalized sphere function-based gas kinetic scheme (GKS) is developed for simulation of two-dimensional compressible viscous flows. This work aims to improve the existing simplified GKS, in which a simple two-dimensional/three-dimensional distribution function is used as the equilibrium state. The present scheme applies the finite volume method to discretize Navier–Stokes equations and the numerical flux at cell interface is evaluated by the local reconstruction of solution for the continuous Boltzmann equation with [Formula: see text]-dimensional sphere function. This local solution contains both the equilibrium part and nonequilibrium part, and the contribution of the nonequilibrium part is controlled by a switch function. It is found that the present scheme has the same expression as the circular function-based GKS for the two-dimensional case and the sphere function-based GKS for the three-dimensional case. Therefore, these two GKSs can be unified, and the developed method provides another way for the simple distribution function.

Numerical Simulation Using a Modified Solver within OpenFOAM for Compressible Viscous Flows

In this work, we attempted to develop an Implicit Coupled Density-Based (ICDB) solver using LU-SGS algorithm based on the AUSM+ up scheme in OpenFOAM. Then sonicFoam solver was modified to include viscous dissipation in order to improve its capability to capture shock wave and aerothermal variables. The details of the ICDB solver as well as key implementation details of the viscous dissipation to energy equation were introduced. Finally, two benchmark tests of hypersonic airflow over a flat plate and a 2-D cylinder were simulated to show the accuracy of ICDB solver. To verify and validate the ICDB solver, the obtained results were compared with other published experimental data. It was revealed that ICDB solver has good agreement with the experimental data. So it can be used as reference in other studies. It was also observed that ICDB solver enjoy advantages such as high resolution for contact discontinuity and low computational time. Moreover, to investigate the performance of modified sonicFoam, a case study of airflow over the prism was considered. Then the results of the modified sonicFoam were compared with the ICDB, rhoCentralFoam and sonicFoam solvers. The results showed that the modified sonicFoam solver possesses higher accuracy and lower computational time in comparison with the sonicFoam and rhoCentralFoam solvers, respectively.