Abstract:
High-order numerical methods, such as the discontinuous Galerkin (DG) method, are widely believed to be superior to traditional low-order schemes for the simulation of turbulent flow problems. However, in the presence of shocks or other discontinuities, the lack of nonlinear stability proves to be a fundamental challenge. Many solutions have been proposed, but most require excessively refined meshes to resolve all the features, which in practice makes numerical simulation difficult. We propose a new method known as high-order implicit shock tracking (HOIST) to tackle this problem, as well as some of the moving mesh techniques required to address this. Only basic knowledge of PDEs will be assumed.
Biography:
Andrew obtained his Bachelor's and Ph.D. degree in Applied Mathematics at the University of California, Berkeley under the joint supervision of Prof. Per-Olof Persson and Prof. Matthew Zahr and is a new postdoctoral instructor at NYU Shanghai under the supervision of Prof. Mathieu Lauriere. Andrew's research interests are in numerical methods for PDEs and mesh generation.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai