SIAC Filtering for Nonlinear Hyperbolic Equations

We present the results of the symmetric and one-sided Smoothness-Increasing Accuracy-Conserving (SIAC) filter applied to a discontinuous Galerkin (DG) approximation for two examples of nonlinear hyperbolic conservation laws. The traditional symmetric SIAC filter relies on having a translation invariant mesh, periodic boundary conditions and linear equations. However, for practical applications that are modelled by nonlinear hyperbolic equations, this is not feasible. Instead we must concentrate on a filter that allows error reduction for nonuniform/unstructured meshes and non-periodic boundary conditions for nonlinear hyperbolic equations. This proceedings is an introductory exploration into the feasibility of these requirements for efficient filtering of nonlinear equations.