Methods for modeling subsurface reservoirs are provided. In at least one embodiment, the process includes building a numerical model of a reservoir having at least one injection well and at least one producing well, and incorporating at least one of an Eulerian boundary condition (EBC) into each of the at least one injection well and at least one producing well, an advanced constitutive model (ACM) int the reservoir, and an adaptive re-meshing technique (ART) into the reservoir model. Then generating a simulation result from the integrated reservoir model, wherein the simulation result includes at least a volume of produced fluids and produced particulate solids from the reservoir, a volume of injected fluids and injected particulate solids into the reservoir, and a simulation of movement of at least a volume of particulate solids and fluids in the reservoir.