A compact subcell WENO limiting strategy using immediate neighbours for Runge-Kutta discontinuous Galerkin methods

Abstract

A compact subcell weighted essentially non oscillatory (CSWENO) limiter is proposed for the solution of hyperbolic conservation laws with discontinuous Galerkin Method which uses only the immediate neighbours of a given cell. These neighbours are divided into the required stencil for WENO reconstruction and an existing WENO limiting strategy is used. Accuracy tests and results for one-dimensional and two-dimensional Burgers' equation and one-dimensional and two-dimensional Euler equations for Cartesian meshes are presented using this limiter. Comparisons with the parent WENO limiter are provided wherever appropriate and the performance of the current limiter is found to be slightly better than the parent WENO limiter for higher orders.

Keywords:

• Discontinuous Galerkin method
• hyperbolic conservation laws
• WENO limiting

2010 AMS Subject Classifications:

• 76J20
• 76L05
• 35L65
• 35L67

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

S. R. Siva Prasad Kochi  http://orcid.org/0000-0001-8974-9760