Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method refines a mesh using the numerical solution of the Navier–Stokes equations computed on the mesh by an open source software Navier2D which implemented a vertex centered finite volume method (FVM) using the median dual mesh to form control volumes about each vertex. The accuracy is shown by the comparison between vortex center locations calculated from the linearly interpolated numerical solutions and those obtained in the benchmark. The AMR method is proposed based on the qualitative theory of differential equations, and it can be applied to refine a mesh as many times as required and used to seek accurate numerical solutions of the mathematical models including the continuity equation for incompressible fluid or steady-state compressible flow with low computational cost.

中文翻译：

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使用低雷诺数的后向步流验证二维自适应网格细化方法的准确性

准确识别流体流动的涡流中心是计算方法的精度度量之一。在验证了二维自适应网格细化 (AMR) 方法在二维盖子驱动型腔流基准中的准确性之后，本文展示了通过二维后向阶梯流基准进行的精度验证。AMR 方法使用开源软件在网格上计算的 Navier-Stokes 方程的数值解来细化网格Navier2D它使用中值对偶网格实现了以顶点为中心的有限体积方法 (FVM)，以形成围绕每个顶点的控制体积。通过比较从线性插值数值解计算的涡旋中心位置与在基准中获得的涡旋中心位置来显示精度。AMR方法是基于微分方程的定性理论提出的，它可以根据需要对网格进行多次细化，并用于寻求数学模型的精确数值解，包括不可压缩流体或稳态的连续性方程可压缩流，计算成本低。