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.