论文标题
Lax Wendroff近似泰勒方法具有快速和优化的加权本质上是非振荡重建的
Lax Wendroff approximate Taylor methods with fast and optimized weighted essentially non-oscillatory reconstructions
论文作者
论文摘要
这项工作的目的是为了将快速的WENO（FWENO）和最佳WENO（Oweno）重建与泰勒方法结合使用，以介绍新的捕获高阶高阶数值方法的新家族，以进行时间离散。 FWENO重建基于平滑度指标，其计算数量比标准的计算次数较低。 Oweno重建是基于非线性权重的定义，该定义允许人们无条件地达到最佳准确性顺序，而不管关键点的顺序如何。近似泰勒方法通过在时间上使用泰勒膨胀来更新数值解决方案，在时间上，不用使用cauchy-kovalevskaya程序，而是通过将空间和时间数值分化与泰勒扩展相结合，以递归方式计算时间衍生物。将这些新方法与基于标准WENO实现和/或SSP-RK时间离散化的方法进行比较。许多测试用例被认为从标量线性1D问题到2D中的非线性保护法系统不等。
The goal of this work is to introduce new families of shock-capturing high-order numerical methods for systems of conservation laws that combine Fast WENO (FWENO) and Optimal WENO (OWENO) reconstructions with Approximate Taylor methods for the time discretization. FWENO reconstructions are based on smoothness indicators that require a lower number of calculations than the standard ones. OWENO reconstructions are based on a definition of the nonlinear weights that allows one to unconditionally attain the optimal order of accuracy regardless of the order of critical points. Approximate Taylor methods update the numerical solutions by using a Taylor expansion in time in which, instead of using the Cauchy-Kovalevskaya procedure, the time derivatives are computed by combining spatial and temporal numerical differentiation with Taylor expansions in a recursive way. These new methods are compared between them and against methods based on standard WENO implementations and/or SSP-RK time discretization. A number of test cases are considered ranging from scalar linear 1d problems to nonlinear systems of conservation laws in 2d.
