A bounded upwinding scheme for computing convection-dominated transport problems

The Eafe Scheme and Cwdd Method for Convection-dominated Problems

Multiscale Analysis for Convection Dominated Transport Equations

In this paper, we perform a systematic multiscale analysis for convection dominated transport equations with a weak diffusion and a highly oscillatory velocity field. The paper primarily focuses on upscaling linear transport equations. But we also discuss briefly how to upscale two-phase miscible flows, in which case the concentration equation is coupled to the pressure equation in a nonlinear ...

Discontinuous Galerkin Methods for Convection-Dominated Problems

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the m...

Hierarchical Matrices for Convection-Dominated Problems

Hierarchical matrices provide a technique to efficiently compute and store explicit approximations to the inverses of stiffness matrices computed in the discretization of partial differential equations. In a previous paper, Le Borne [2003], it was shown how standard H-matrices must be modified in order to obtain good approximations in the case of a convection dominant equation with a constant c...

Numerical Methods for Scalar Convection-Dominated Problems