In this paper, a new scheme of arbitrary high order accuracy in both space and time is proposed to solve hyperbolic conservative laws. Based on the idea of flux vector splitting(FVS) scheme, we split all the space and time derivatives in the Taylor expansion of the numerical flux into two parts: one part with positive eigenvalues, another part with negative eigenvalues. According to a Lax-Wendroff procedure, all the time derivatives are then replaced by space derivatives. And the space derivatives is calculated by WENO reconstruction polynomial. One of the most important advantages of this new scheme is easy to implement.In addition, it should be pointed out, the procedure of calculating the space and time derivatives in numerical flux can be used as a building block to extend the current first order schemes to very high order accuracy in both space and time. Numerous numerical tests for linear and nonlinear hyperbolic conservative laws demonstrate that new scheme is robust and can be high order accuracy in both space and time.
Recasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-Projection-type method for gas dynamics
Arbitrary high order splitting methods for linear Schr{ö}dinger equations with non-trivial compatibility conditions
Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL（南特大学、法国国家科学研究中心、让·勒雷数学实验室）；Université de Genève, Section de mathématiques（日内瓦大学数学系）
Runge-Kutta Discontinuous Galerkin Method Based on Flux Vector Splitting with Constrained Optimization-based TVB(D)-minmod Limiter for Solving Hyperbolic Conservation Laws
Low-regularity error estimates of a filtered Lie-Trotter splitting scheme for the Zakharov system in arbitrary dimensions
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Sorbonne Université（索邦大学）；Tsinghua University（清华大学）
Artificial diffusion for convective and acoustic low Mach number flows II: Application to Liou-Steffen, Zha-Bilgen and Toro-Vasquez convection-pressure flux splittings
Liou-Steffen分裂（AUSM）格式在低马赫数模拟中很受欢迎，然而，与许多可压缩流的数值格式一样，它们需要仔细修改以精确地解决该区域的对流特性。以前的分析，这些计划通常只集中在一个单一的离散计划在对流限制，只考虑流动与声学效应的经验，如果在所有。在我们最近的论文Hope-Collins & di Mare（2023）中，我们推导出了对低马赫数格式的人工扩散标度的约束条件，这些约束条件适用于有和没有声学效应的流动，并将这一分析应用于Roe型有限体积格式。在本文中，我们形成近似的扩散矩阵的Liou-Steffen分裂，以及密切相关的Zha-Bilgen和Toro-Vasquez分裂。我们使用Hope-Collins & di Mare，2023中的约束条件，推导并分析了低马赫数时每个分裂所需的标度。通过将扩散矩阵转换为熵变量，我们可以识别与Hope-Collins & di Mare，2023中使用的理想形式相比错误的扩散项。这些项在Liou-Steffen分裂中渐近消失，但在Zha-Bilgen和Toro-Vasquez分裂中会产生虚假的熵，除非使用特定形式的界面压力。声学和对流的数值例子验证了分析的结果，并显示了评估这种类型的计划时，考虑熵场的分辨率的重要性。
