非线性声波方程的时间显式混合高阶方法

IF 1.9 3区 数学 Q2 Mathematics
Morgane Steins, A. Ern, O. Jamond, Florence Drui
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引用次数: 0

摘要

我们设计了非线性声波方程在时间上的二阶形式的完全显式格式,使用HHO方法进行空间离散,使用leapfrog格式进行时间积分。说明的关键思想是在每个时间步近似单元和面之间的静态非线性耦合的迭代过程。该过程基于HHO稳定算子的分裂,并且在线性情况下,证明了在足够大的稳定权重下均匀收敛于网格尺寸。结果表明,增加稳定重量对CFL条件的影响适中。数值实验表明,与半隐式分割方法相比,该分割方法对单元和面未知静态耦合的计算效率更高。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Time-explicit Hybrid High-Order method for the nonlinear acoustic wave equation
We devise a fully explicit scheme for the nonlinear acoustic wave equation in its second-order formulation in time, using the HHO method for space discretization and the leapfrog scheme for time integration. The key idea for the explicitation is an iterative procedure to approximate at each time step the static nonlinear coupling between the cell and face unknowns. This procedure is based on a splitting of the HHO stabilization operator and, in the linear case, is proved to converge for a large enough weight of the stabilization uniformly in the mesh size. Increasing the stabilization weight turns out to have a moderate impact on the CFL condition. The numerical experiments demonstrate the computational efficiency of the splitting procedure compared to a semi-implicit scheme for the static coupling between cell and face unknowns.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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