论文标题
分散波方程的一系列保守数值方法
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
论文作者
论文摘要
我们开发了一个通用框架，用于设计基于零件操作员的总和和空间中的拆分形式的保守数值方法，并及时使用Runge-Kutta方法。我们将此框架应用于几种非线性分散波方程的全差异保守方法：Benjamin-Bona-Mahony（BBM），Fornberg-Whitham，Camassa-Holm，Degasperis-Procesi，Holm-Hone，Holm-Hone和BBM-BBM-BBM-BBM BBM BBM System。这些完整的离散化保留了每个系统的所有线性不变性和一个非线性不变性。空间半差异包括有限的差异，光谱搭配以及不连续和连续的有限元方法。使用松弛runge-kutta方法，时间离散基本上是明确的。我们从派生类中实施了一些特定方案，并通过数值测试来证明其有利的属性。
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes of fully-discrete conservative methods for several nonlinear dispersive wave equations: Benjamin-Bona-Mahony (BBM), Fornberg-Whitham, Camassa-Holm, Degasperis-Procesi, Holm-Hone, and the BBM-BBM system. These full discretizations conserve all linear invariants and one nonlinear invariant for each system. The spatial semidiscretizations include finite difference, spectral collocation, and both discontinuous and continuous finite element methods. The time discretization is essentially explicit, using relaxation Runge-Kutta methods. We implement some specific schemes from among the derived classes, and demonstrate their favorable properties through numerical tests.
