Eulerian—Lagrangian solution of convection dominated diffusion problems

Abstract

Some existing finite difference methods for the numerical solution of convection dominated diffusion equations are compared. Two semi‐implicit methods, Lagrangian based and applied on an Eulerian grid system, are then derived and discussed. The new methods are demonstrated to be transportive and unconditionally stable. Moreover, the artificial diffusion and the spurious oscillations of these methods are also analysed and compared. Extensions to n‐space variables and to non‐linear equations are indicated, along with various applications.