基于最小二乘的单元中心拉格朗日流体动力学节点格式
A least-squares based nodal scheme for cell-centered Lagrangian hydrodynamics
摘要：
本文提出了一种新的、有效的拉格朗日格式的节块格式。在最小二乘意义下，通过节点求解器计算单元顶点处的单个压力和速度，并使用这两个变量来评估穿过单元界面的数值通量。由此产生的节点速度也负责移动网格。通过有限体积离散中的几个数值例子研究了该方法的准确性和鲁棒性，并与其他两种节点Riemann求解器进行了比较。结果表明，它的性能与后两者相当。虽然目前的文件主要集中在一阶有限体积（FV），其扩展到高阶方法，如高阶FV，间断Galerkin（DG）或重建间断Galerkin（rDG），是相当简单的。该方法具有易于推广到三维的特点。
英文摘要：
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.
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