Speaker
Pei Fu, Nanjing University of Aeronautics and Astronautics
Abstract
In this talk, we present a family of high order cut finite element methods based on the discontinuous Galerkin (DG) framework for hyperbolic problems. To avoid the small-cut-cell issue, a ghost penalty stabilization is employed to stabilize the scheme. The strong stability-preserving Runge–Kutta method is used for time discretization, in which the time step is chosen independently of the size of the cut elements. We show that the proposed methods possess stability and accuracy properties as the standard DG methods on fitted meshes. We also prove and verify that the scheme preserves the bound-preserving property for scalar conservation laws and Euler equations when a bound-preserving limiter is applied. Numerical experiments demonstrate that the proposed methods achieve high-order accuracy for smooth solutions and perform well for problems with discontinuities.