Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
Sebastian Bleecke, Abhijit Biswas, David I. Ketcheson, Hendrik Ranocha, Jochen Schutz
我们研究Gavrilyuk和Shyue(2022)最近提出的Benjamin-Bona-Mahony(BBM)方程的双曲近似。 我们开发无症状保存数值方法使用隐式显式(附加)的 Runge-Kutta 方法,这些方法在刚性线性部分中隐含。 超栓化的新离散化保存了重要的不变性融合到BBM方程的不变性。 我们使用熵松弛的方法来使完全离散的方案节能。 数字实验证明了这些离散的有效性。
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods using implicit-explicit (additive) Runge-Kutta methods that are implicit in the stiff linear part. The new discretization of the hyperbolization conserves important invariants converging to invariants of the BBM equation. We use the entropy relaxation approach to make the fully discrete schemes energy-preserving. Nume...
