The Material Point Method (MPM) is a hybrid Eulerian-Lagrangian approach, which uses moving material points and computational nodes on a background mesh. This approach is very effective particularly in the context of large deformations.
The Lattice Boltzmann equation Method (LBM) is a meso-scale fluid solver for modeling grain-scale fluid flow. The Discrete-Element Method (DEM) is coupled with LBM to model soil-fluid interactions at particulate scale.
Dual Lattice Model (DLM) is a novel technique which involves coupling the solid lattice system and the fluid lattice system (Figure 2) to model the multi-physics problem.