Abstract A stable and non-dissipative numerical scheme for Cartesian methods is proposed. The proposed scheme is based on the second-order kinetic energy and entropy preserving scheme, which the authors proposed recently, and conservation is satisfied at non-conforming boundaries where the grid refinement level is different across the computational block boundaries. In the proposed scheme, ghost cells are used at computational block boundaries for efficient parallel computation, and conservation is satisfied by assigning appropriate values to the ghost cells. Also, although the five conservative variables (i.e., mass, momentum, and total energy) are typically transferred from computational cells to corresponding ghost cells at computational block boundaries, the proposed scheme transfers two more conservative variables to satisfy conservation at non-conforming block boundaries. In a vortex convection test, the convergence rates of the L2- and L∞-error norms are examined, and the proposed scheme preserves the second-order of accuracy without inducing destructive errors at non-conforming boundaries. In an inviscid Taylor-Green vortex simulation, the proposed scheme demonstrates superior numerical stability by preserving kinetic energy and entropy. Also, the proposed scheme performs more stable computations on a non-conforming computational grid than a typical kinetic energy preserving scheme calculated on a uniform computational grid.

中文翻译：

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笛卡尔网格上非一致块边界的稳定和非耗散动能和熵保持 (KEEP) 方案

摘要 针对笛卡尔方法提出了一种稳定且无耗散的数值方案。所提出的方案基于作者最近提出的二阶动能和熵保持方案，并且在非一致边界处满足守恒，其中网格细化级别跨计算块边界不同。在所提出的方案中，在计算块边界处使用鬼细胞以进行有效的并行计算，并且通过为鬼细胞分配适当的值来满足守恒。此外，虽然五个保守变量（即质量、动量和总能量）通常从计算单元转移到计算块边界处的相应虚单元，提议的方案转移了两个更保守的变量来满足不符合块边界的守恒。在涡流对流测试中，检查了 L2 和 L∞ 误差范数的收敛速度，并且所提出的方案保持了二阶精度，而不会在不符合边界处引起破坏性误差。在无粘性 Taylor-Green 涡流模拟中，所提出的方案通过保留动能和熵证明了优异的数值稳定性。此外，与在均匀计算网格上计算的典型动能保持方案相比，所提出的方案在非一致计算网格上执行更稳定的计算。并且所提出的方案保持了二阶精度，而不会在不符合的边界处引起破坏性错误。在无粘性 Taylor-Green 涡流模拟中，所提出的方案通过保留动能和熵证明了优异的数值稳定性。此外，与在均匀计算网格上计算的典型动能保持方案相比，所提出的方案在非一致计算网格上执行更稳定的计算。并且所提出的方案保持了二阶精度，而不会在不符合的边界处引起破坏性错误。在无粘性 Taylor-Green 涡流模拟中，所提出的方案通过保留动能和熵证明了优异的数值稳定性。此外，与在均匀计算网格上计算的典型动能保持方案相比，所提出的方案在非一致计算网格上执行更稳定的计算。