A Cartesian, adaptively refined and staggered grid, monolithic incompressible multiphase flow solver for high density and high shear particle-laden flows

Multiphase flows in presence of particulate matter are ubiquitous in natural and industrial processes. However, such flows are quite challenging to model computationally especially for high density and high viscosity contrasting fluids. Naive discretization of the incompressible Navier-Stokes (INS) equations fail miserably due to interfacial instabilities for high density and high shear flows. At the same time the spatially varying coefficients lead to a complicated linear system which is hard to solve implicitly. In this work we overcome both these limitations by employing a consistent and well-balanced discretization of the INS equations which is solved as a monolithic system on staggered, Cartesian and adaptively refined grids. The spatio-temporal discretization remains stable for upto six order of magnitude contrast between density and viscosity coefficients. We present several convergence and order-of-accuracy results, as well as two phase and three phase fluid-structure interaction examples. The fluid-fluid interface is captured on the Eulerian grid using level set method, whereas the immersed particulate matter is fully resolved via the immersed boundary method.