论文标题
以细胞为中心的Lagrangian流体动力学的基于最小二乘的节点方案
A least-squares based nodal scheme for cell-centered Lagrangian hydrodynamics
论文作者
论文摘要
本文提出了一种新的，有效的淋巴结方案，用于在拉格朗日公式中以细胞为中心的可压缩流。在最小二乘中，通过节点求解器计算单个压力和细胞顶点的速度，并且两个变量都用于评估细胞界面上的数值通量。由此产生的节点速度也负责移动网格。通过有限体积离散化的几个数值示例研究了所提出方法的准确性和鲁棒性，并与其他两个Nodal Riemann求解器进行了比较。结果表明，其性能与后两个相媲美。尽管目前的纸主要集中于一阶有限体积（FV），但其扩展到高阶方法，例如高阶FV，不连续的Galerkin（DG）或重建的不良盖尔金（RDG），非常简单。并且该方法具有易于扩展到三个维度的能力。
This paper presents a new and efficient nodal scheme for cell-centered compressible flows in Lagrangian formulation. A single pressure and the velocity at cell vertex are computed by the nodal solver in a least-squares sense, and both variables are used to evaluate the numerical flux across the cell interface. The resulting nodal velocity is also responsible for moving the mesh. The accuracy and robustness of the proposed method is studied by several numerical examples in the finite volume discretization, and compared with two other nodal Riemann solvers. It is shown that its performance is comparable to the latter two. Although the current paper mainly focuses on the first-order finite volume (FV), its extension to higher order methods such as high-order FV, discontinuous Galerkin (DG) or reconstructed discontinous Galerkin (rDG), is quite straightforward. And this method has the capability of easily extending to three dimensions.
