发表机构
Indian Institute of Science（印度科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无法识别接触间断的 PVU Boltzmann 格式，通过重新设计 peculiar velocity 项的离散，使数值扩散仅依赖 bulk 速度，实现了 1D 接触间断和 2D 滑移面的精确捕获，同时保持低扩散和稳健性。
AI 中文摘要
本文从基于 peculiar velocity 的上风（PVU）Boltzmann 格式这一稳健基础出发，该格式无法识别接触间断，针对气体动力学方程的数值解引入了新的变体。对原始格式的修正偏微分方程（MPDE）分析表明，对应于 peculiar velocity 部分的数值扩散系数在 Mach 数趋于零时并不消失。重新设计了 peculiar velocity 项的数值离散，使得数值扩散仅依赖于穿过静止接触间断的 bulk 流体速度，从而能够在 1D 中精确捕获接触间断，在 2D 中精确捕获滑移面。所得的变体在保持原始格式稳健性的同时实现了低数值扩散，这通过多个 1D 和 2D 基准可压缩流动测试案例得到了验证。
英文摘要
Starting from the robust foundation of the peculiar velocity based upwind (PVU) Boltzmann scheme, which fails to recognize contact discontinuities, this paper introduces new variants for the numerical solutions of equations of gas dynamics. A modified partial differential equation (MPDE) analysis of the original scheme reveals that the numerical diffusion coefficient corresponding to the peculiar velocity part does not vanish as the Mach number goes to zero. The numerical discretization of the peculiar velocity term is redesigned so that the numerical diffusion depends only on the bulk fluid velocity across the stationary contact discontinuities, enabling its exact capture in 1D and exact capture of slip surfaces in 2D. The resulting variants achieve low numerical diffusion while preserving the robustness of the original scheme, as demonstrated through several 1D and 2D benchmark compressible flow test cases.
