We present a discussion on how one can simulate sand as a continuum using elastoplasticity. We showed the efficacy of Drucker-Prager plasticity model and St. Venant Kirchhoff with Hencky strain to model sand. We discretized the continuum equation using Material Point Method (MPM). We also present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use Material Point Method to discretize the governing equations. We use two grids, corresponding to water and sand phase. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop an improved return mapping for sand plasticity that prevents volume gain artifacts in the traditional Drucker-Prager model.

Finally, we revisit the problem of redistancing, which is native to the level set paradigms. We used an interesting alternative view that utilizes the Hopf-Lax formulation of the solution to the eikonal equation, as proposed by \cite{lee:2017:revisiting,darbon:2016:algorithms}. In this approach, the signed distance at an arbitrary point is obtained without the need of distance information from neighboring points. We extend the work of Lee et al. \cite{lee:2017:revisiting} to redistance functions defined via interpolation over a regular grid.