HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS
HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS
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发表时间：
2007
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通讯作者：
J. Qiu;J. Qiu
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作者：
J. Qiu;J. Qiu
在本文中，我们使用Hermite加权本质无振荡（HWENO）格式与Lax-Wendroff时间离散程序，称为HWENO-LW格式，解决Hamilton-Jacobi方程。HWENO格式中的重构思想来自于原始韦诺格式，然而函数及其一阶导数值都随时间演化并用于重构。HWENO格式的一个主要优点是它在重建时的紧凑性。我们探讨的可能性，在避免非线性权重的过程中的一部分，从而降低成本，但仍然保持非振荡性质的问题与强不连续的衍生物。结果表明，HWENO-LW格式与Qiu和Shu [19]的HWENO-Runge-Kutta时间离散格式（HWENO-RK）相比，其主要优点是计算量小，重构过程紧凑。大量的数值实验来说明该方法的能力。数学学科分类：65 M06、65 M99、70 H20。
In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with HWENO with Runge-Kutta time discretizations schemes (HWENO-RK) of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method. Mathematics subject classification: 65M06, 65M99, 70H20.