Nonstandard Eulerian–Lagrangian methods for multi-dimensional reactive transport problems Original Research Article

We propose new Eulerian–Lagrangian numerical methods that efficiently handle the numerically difficult convection-dominated transport problems with nonlinear reactions. The nonstandard techniques are based on a nonlocal treatment of nonlinear reaction terms and more sophisticated discretizations of time derivatives. We define the numerical solution of the convection–reaction part of the transport equation using an “exact” time-stepping scheme. Standard finite differences are used for solving the remaining dispersion part. This approach leads to significant, qualitative improvements in the behavior of the numerical solutions. The relative importance of convection, and biological and chemical reactions are directly incorporated into the corresponding numerical schemes.