Eulerian–Lagrangian time-stepping methods for convection-dominated problems

The accuracy and efficiency of several lower and higher order time integration schemes in Eulerian–Lagrangian computations are investigated for solution of convection–diffusion problems with nonlinear reaction terms. The implementation of these schemes differs from their Eulerian counterparts in the fact that they are applied during each time step, along the characteristic curves rather than in the time direction. The major focus is to examine the computational characteristics of a class of implicit, explicit, and implicit–explicit time marching methods combined with the Eulerian–Lagrangian procedure. The obtained results for several benchmark problems are considered to be representative, and might be helpful for a fair rating of solution schemes, particularly in long time computations.

Keywords:

• Convection–diffusion problems
• Eulerian–Lagrangian methods
• Runge–Kutta schemes
• Time stepping