**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Friday, August 16, 2019 11:00 AM EDT

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.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.