论文标题
将操作员拆分求解器将求解器拆分为基于标准的有限体积通量算法。 Lagrange预测型方法的气体动力学方法
Recasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-Projection-type method for gas dynamics
论文作者
论文摘要
在本文中，我们提出了对声学传输操作员分裂的拉格朗格预测方法的修改，以模拟重力。原始方法涉及两个步骤，分别解释了声学和传输效应。我们的工作提出了对运输步骤的简单修改，结果修改后的方案被证明是一种漏气方法。这种新的数值方法在计算上的昂贵，内存效率更高，并且比原始方法更易于实现。我们通过证明在经典的CFL条件下证明该方法可确保质量，能量和熵满足的阳性。该方法的柔性磁通结构可以使该方法的直接扩展能够直接扩展到多维问题（相对于空间）和这项工作中介绍的高阶离散化。我们还提出了将通量分解求解器作为松弛近似的解释。对新方法的稳定性和准确性都针对一维和二维数值实验进行了测试，这些实验涉及高度可压缩的流量和低操作机制。
In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic and transport effects. Our work proposes a simple modification of the transport step, and the resulting modified scheme turns out to be a flux-splitting method. This new numerical method is less computationally expensive, more memory efficient, and easier to implement than the original one. We prove stability properties for this new scheme by showing that under classical CFL conditions, the method is positivity preserving for mass, energy and entropy satisfying. The flexible flux-splitting structure of the method enables straightforward extensions of the method to multi-dimensional problems (with respect to space) and high-order discretizations that are presented in this work. We also propose an interpretation of the flux-splitting solver as a relaxation approximation. Both the stability and the accuracy of the new method are tested against one-dimensional and two-dimensional numerical experiments that involve highly compressible flows and low-Mach regimes.
