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The goal of this sub-project is to develop open-source software that is capable of simulating particles in a fluid (on different scales). The simulations will make use of two already existing open source software packages MercuryDPM and oomph-lib. There are many methods for coupling particles and fluids, which resolved the dynamics on different scales; however, due to the size of problems considered by this project we will focus on under-resolved fluid-particle methods.

In under-resolved methods, the fluid elements are larger than the particle size. The fluid in these methods are mostly modeled by the local averaged Navies-Stokes formulation, first presented by Anderson and Jackson. This model accounts for the particle phase by defining a porosity which is the percentage of fluid at a given position. Numerical methods to solve under-resolved model can be categorized in two different groups, Eulerian and Lagrangian. The Eulerian methods are methods that solve the local averaged Naiver-Stokes equations on a mesh with methods such as FEM or FVM. The Lagrangian methods solve the fluid phase by using mesh-less methods e.g. SPH, MPS or Mesh-Free Galerkin Methods. We will use a monolithically coupled FEM-DPM numerical method for our under-resolved case.