Development of Cartesian Grid Method and Local Grid Refinement for Discrete Velocity Method (Communications in Computational Physics, 2025)
Cartesian grid method and local grid refinement for discrete velocitymethod (DVM) are developed in this work, with the numerical flux of DVM constructed by semi-Implicit Richtmyer method. To implement the boundary condition,the interpolation approach is applied, where the distribution function at the fluid sideof the boundary point is first approximated by interpolation method given the knowledge of the boundary point. Once the distribution function is interpolated, the reflected Maxwellian distribution and numerical flux at boundary point can be evaluated. Then the distribution function at the fluid point close to the boundary can beupdated by finite difference formulation. However, the interpolation of the distribution function at the boundary point is a significant challenge as the breakdown of theupwind stencil will cause instability. To preserve the upwind stencil, the most effectiveapproach is to perform interpolation along the characteristic lines. Moreover, the localgrid refinement is introduced to reduce the computational cost for industrial application. To validate the proposed Cartesian grid method, some numerical examples aresimulated. The results demonstrate the accuracy and stability of the present methodfor straight boundary with oblique and curved boundary, subsonic and supersonicflows.