We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a Mixed method using H(div) spaces for the diffusive terms. Furthermore, hybridization is used to reduce the number of globally coupled degrees of free...

A new high-resolution scheme is developed for convection–diffusion problems in domains with moving boundaries. A finite element approximation of the governing equation is designed within the framework of a conservative Arbitrary Lagrangian Eulerian (ALE) formulation. An implicit flux-corrected transport (FCT) algorithm is implemented to suppress spurious undershoots and overshoots appearing in ...

We discuss the application of the finite element method to the numerical solution of scalar two–dimensional steady convection–diffusion equations with the emphasis on upwinding techniques satisfying the discrete maximum principle. Numerical experiments in convection–dominated case indicate that the improved Mizukami–Hughes method is the best choice for solving the mentioned class of problems us...

In this paper, we study the numerical solution of optimal control problems governed by a system of convection diffusion PDEs with nonlinear reaction terms, arising from chemical processes. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used for discretization. Residual-based error estimators are used for the state, the adjoint and the control var...

We study stabilization methods for the discretization of convection-dominated elliptic convection-diffusion problems by linear finite elements. It turns out that there exist close relations between a new version of stabilization via local projection and the continuous interior penalty method. AMS Subject Classifications: 65 N15, 65N30, 65N12

A wide class of mass transfer problems is governed by the combined effect of convection, diffusion and reaction (CDR) processes. The finite element method using the standard Bubnov Galerkin method based on linear elements is widely applied for diffusion-dominated problems where the method produces accurate results. However, at high Pé clet numbers of transport problems, where the convection pro...

This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the isotropic HelmholtzFourier (HF) transform and series, the Helmholtz-Laplace (HL) transform, and the anisotropic convection-diffusion wavelets and ridgelets. The lat...

Systems of convection–diffusion equations model a variety of physical phenomena which often occur in real life. Computing the solutions of these systems, especially in the convection dominated case, is an important and challenging problem that requires development of fast, reliable and accurate numerical methods. In this paper, we propose a second-order fast explicit operator splitting (FEOS) m...

The diffusion coefficients at control volume surfaces are required in the most-widely used finite-volume method for numerical simulation of convection-diffusion equations. Various interpolation methods for diffusion coefficients at control volume surfaces are briefly discussed and extensively compared with the analytical solutions of both pure diffusion and convection-diffusion problems in this...

We present a new splitting method for time-dependent convention-dominated diffusion problems. The original convention diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. A few important features of the scheme lie in the facts that the convection subproblem is sol...