Computational modelling of severe gradients with mass operator constructions
A generalized mass operator construction is developed from the Galerkin finite element method and used to compute problems with severe internal gradients as simple models for the frontal process. The generalized mass operator construction is compared with four-point upwind differencing of the advective terms. When combined with Crank-Nicolson time differencing both schemes provide optimal choices for generating accurate solutions with severe gradients, primarily by controlling dispersion errors. For very severe gradients the generalized mass operator construction produces more accurate solutions. For severe internal gradients controlled by nonlinear advection it is necessary to supplement the optimal mass operator scheme with a flux-based numerical dissipation incorporating an internal limiter.
scientific article; zbMATH DE number 4057177
scientific article