PhD Pre-comprehensive Seminar | Krishna Dutt, Limiting on Triangular Meshes for Discontinuous Galerkin Method

Friday, August 16, 2019 11:00 am - 11:00 am EDT (GMT -04:00)

MC 6460


Krishna Dutt | Applied Math, University of Waterloo


Limiting on Triangular Meshes for Discontinuous Galerkin Method


Nonlinear hyperbolic conservation laws govern many complex phenomena like shock-shock, shock-vortex interactions, fluid flow around a turbine etc. Higher order numerical schemes like the discontinuous Galerkin (DG) method are being progressively used in computational fluid dynamics (CFD) codes to solve such conservation laws. Numerical solutions obtained using higher order methods often develop spurious oscillations, which may lead to instabilities in the solution. Slope limiting is one of the mechanism sused to suppress such oscillations, thereby stabilizing the numerical solution. Limiters were originally proposed for Finite Volume (FV) methods, where restrictions are imposed on the reconstructed slope to maintain second order accuracy and stability. Limiters tailored specifically for the DG method have also been proposed. For e.g., a new moment limiter was proposed for unstructured triangular meshes, which works by finding the directions in which the linear solution coefficients decouple and reconstructing the coefficients along these directions using one-dimensional limiters. However, most standard limiters are designed for conformal meshes i.e; each triangular element in the mesh has three other triangular elements sharing an edge with it. The present research involves extending these limiters to nonconforming meshes which arise in hp adaptive computations on a graphics processing unit.