a cell-centered ale method with hllc-2d riemann solver in 2d cylindrical geometry

This paper presents a second-order direct arbitrary Lagrangian Eulerian (ALE) method for compressible flow in two-dimensional cylindrical geometry. This algorithm has half-face fluxes and a nodal velocity solver, which can ensure the compatibility between edge fluxes and the nodal flow intrinsically. In two-dimensional cylindrical geometry, the control volume scheme and the area-weighted scheme are used respectively, which are distinguished by the discretizations for the source term in the momentum equation. The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law (MUSCL) on unstructured meshes. Numerical results are provided to assess the robustness and accuracy of these new schemes.

本文提出了一种用于二维柱几何可压缩流的二阶直接任意拉格朗日 - 欧拉（ALE）方法。该算法具有半面通量和节点速度求解器，能够从本质上确保边通量与节点流之间的兼容性。在二维柱几何中，分别使用了控制体积格式和面积加权格式，它们通过动量方程中源项的离散化来区分。通过在非结构化网格上采用单调上游守恒律格式（MUSCL）构建了这些格式的二维二阶扩展。给出了数值结果以评估这些新格式的稳健性和准确性。