论文标题
双曲线保护法的LAX-WENDROFF通量重建法
Lax-Wendroff flux reconstruction method for hyperbolic conservation laws
论文作者
论文摘要
LAX-WENDROFF方法是一种单个步骤方法，用于与偏微分方程支配的时间相关的解决方案，与每个时间步长需要多个阶段的Runge-Kutta方法相比。我们开发了该方法的通量重建版本，并与适用于一般双曲线保护法的无雅可比亚式laxwendroff程序结合使用。该方法是搭配类型，是不含正交的，可以用矩阵和向量操作来施放。特别关注数值通量的构建，包括针对非线性问题，导致CFL数量高于现有方法，这是通过傅立叶分析和所有订单的均匀性能所显示的。给出了线性和非线性问题的数值结果，以证明该方法的性能和准确性。
The Lax-Wendroff method is a single step method for evolving time dependent solutions governed by partial differential equations, in contrast to Runge- Kutta methods that need multiple stages per time step. We develop a flux reconstruction version of the method in combination with a Jacobian-free Lax- Wendroff procedure that is applicable to general hyperbolic conservation laws. The method is of collocation type, is quadrature free and can be cast in terms of matrix and vector operations. Special attention is paid to the construction of numerical flux, including for non-linear problems, resulting in higher CFL numbers than existing methods, which is shown through Fourier analysis and yielding uniform performance at all orders. Numerical results up to fifth order of accuracy for linear and non-linear problems are given to demonstrate the performance and accuracy of the method.
