Comparison of artificial-dissipation and solution-filtering stabilization schemes for time-accurate simulations

Abstract

The current study investigates the use of solution filtering and artificial dissipation as stabilization methods for time-accurate computations, notably focusing on how the decoupling of dissipation from integration impacts simulation error. Rewriting solution filtering in an effective artificial-dissipation form explicitly reveals the issue of temporal inconsistency, which is addressed by a proposed CFL re-scaling. In addition, expressing symmetric discrete filters as difference operators inspires the derivation of a “filter-based” artificial-dissipation formulation that provides the opportunity for direct spectral manipulation by utilizing known filter stencil specifications; this furthermore facilitates the creation of Padé-type artificial dissipation terms with spectrally tunable and scale-discriminant properties. Damping characteristics of the schemes are assessed through von Neumann analysis and are confirmed via simulations of the one-dimensional advection equation (wave-packet transport) as well as the three-dimensional compressible Navier–Stokes system (Taylor–Green vortex), where the impact of time step size on accuracy of the respective stabilization techniques is inspected.