论文标题
在不连续的有限元方法中进行冲击捕获的Riemann差异方案
A Riemann Difference Scheme for Shock Capturing in Discontinuous Finite Element Methods
论文作者
论文摘要
我们提出了一种新型的具有结构性的数值方案，用于非线性双曲系统的不连续有限元近似值。该方法可以理解为对高阶交错网格的宽松液化通量的概括，并且不取决于任何可调参数。在一组条件下，我们表明该方法是保守和不变的域。 Euler方程上的数值实验表明，该方案解决不连续性的能力而不引入过多的虚假振荡或耗散。
We present a novel structure-preserving numerical scheme for discontinuous finite element approximations of nonlinear hyperbolic systems. The method can be understood as a generalization of the Lax-Friedrichs flux to a high-order staggered grid and does not depend on any tunable parameters. Under a presented set of conditions, we show that the method is conservative and invariant domain preserving. Numerical experiments on the Euler equations show the ability of the scheme to resolve discontinuities without introducing excessive spurious oscillations or dissipation.
