Fourier analysis of semi-discrete and space–time stabilized methods for the advective–diffusive–reactive equation: II. SGS

Abstract

In this paper, stability and accuracy of various transient subgrid scale (SGS) stabilized methods are analyzed for the advection–diffusion–reaction equation. The methods studied are based on semi-discrete and time-discontinuous space–time versions of the SGS method, an approximation of the variational multiscale method. Also, predictor multi-corrector algorithms of the above methods are analyzed. Within this context, the diagonally implicit treatment of dissipative source terms, which was shown in the first paper of the series to enhance both, stability and accuracy of explicit methods, is explored in this paper for the SGS method. It will be shown that the parent SUPG and SGS methods perform very similarly. That mass lumping may improve the accuracy of explicit methods. And finally, the most attractive options for the explicit integration of equations with source terms will be presented.