Time accurate consistently stabilized mesh-free methods for convection dominated problems

Dual-Mesh Characteristics for Particle-Mesh Methods for Convection-Dominated Di usion Problems

Particle-in-cell (PIC) methods have been emerged as a powerful computational tool for the simulation of convection-dominated ows. The basic idea of the method is to introduce computational particles each of which is given a nite size and represents a large number of physical particles with similar properties. The convection part of the ow can be performed by moving the particles along the chara...

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...

Numerical Methods for Scalar Convection-Dominated Problems

Discontinuous Galerkin multiscale methods for convection dominated problems

We propose an extension of the discontinuous Galerkin multiscale method, presented in [11], to convection dominated problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the discontinuous Galerkin method allows us to better cope with multiscale features as well as boundary layers in the solution. In the proposed method the trail and tes...

Multilevel Homotopic Adaptive Methods for Convection Dominated Problems

A multilevel homotopic adaptive method is presented in this paper for convection dominated problems. By the homotopic method with respect to the diffusion parameter, the grids are iteratively adapted to better approximate the solution. Some new theoretic results and practical techniques for the grid adaptation are presented. Numerical experiments show that a standard finite element scheme based...