Numerical Analysis Seminar

Date: April 25, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Jesse Chan, Rice University

Title: Discretely entropy stable high order methods for nonlinear conservation laws

Abstract: High order methods offer several advantages in the approximation of solutions of nonlinear conservation laws, such as 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. Provably stable finite difference methods based on summation-by-parts (SBP) operators and a concept known as flux differencing address this inherent instability by ensuring that the solution satisfies a semi-discrete entropy inequality. In this talk, we discuss how to construct discretely entropy stable high order discontinuous Galerkin methods by generalizing entropy stable finite difference schemes using discrete L2 projection matrices and “decoupled” SBP operators. Extensions to curvilinear meshes will be also discussed, and numerical experiments for the one and two-dimensional compressible Euler equations confirm the semi-discrete stability and high order accuracy of the resulting methods.