Entropy stable high order discontinuous Galerkin methods for nonlinear conservation laws
- 4:30PM at REC 114
- Prof. Jesse Chan, Rice University
- Entropy stable high order discontinuous Galerkin methods for nonlinear conservation laws
Abstract: High order discontinuous Galerkin (DG) methods offer several advantages in the approximation of solutions of nonlinear conservation laws, such as geometric flexibility, improved accuracy, and low numerical dispersion/dissipation. However, these methods also tend to suffer from instability in practice, requiring filtering, limiting, or artificial dissipation to prevent solution blow up. Entropy stable schemes address one primary cause of this instability by utilizing summation-by-parts (SBP) finite difference operators and an approach called flux differencing to ensure that the solution satisfies a semi-discrete entropy inequality. In this talk, we show that high order DG methods can be re-interpreted within an SBP framework using discrete projection and “decoupled” SBP operators, and utilize this equivalence to construct semi-discretely entropy stable schemes on meshes of simplicial and tensor product elements.