Genuinely nonlinear models for convection-dominated problems

Genuinely Nonlinear Models for Convection-dominated Problems

This paper introduces a general, nonlinear subgrid-scale (SGS) model, having bounded artiicial viscosity, for the numerical simulation of convection-dominated problems. We also present a numerical comparison (error analysis and numerical experiments) between this model and the most common SGS model of Smagorinsky, which uses a p-Laplacian regularization. The numerical experiments for the 2-D co...

A Nonlinear Subgrid–Scale Model for Convection Dominated, Convection Diffusion Problems

We present a nonlinear subgrid–scale method for the stabilization of the Galerkin approximation to convection dominated, convection diffusion problems, establish existence and uniqueness results, and provide an a priori error estimate for the method. ∗email: [email protected], Department of Mathematical Sciences, Clemson University, Clemson S.C. 29634 †email: [email protected], Department of...

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