Scalable two-phase flow solvers

Two-phase flows arise in many areas of application such as in the study of coastal and hydraulic processes. Often the fluids involved can be modelled by incompressible phases which have disparate physical properties such as density and viscosity. We utilise a two-phase flow model of immiscible Newtonian fluids. A key part of this model is a set of variable coefficient NavierâStokes equations. This thesis focuses on the numerical solution of the linear systems which arise after linearisation of these equations. Solving these systems often dominates the computation time when running simulations. One of the challenges in solving the model is that the density and viscosity coefficients are discontinuous and can have large jumps between the two phases. In this work we consider preconditioned iterative Krylov methods to solve the large and sparse linear systems and pay particular attention to incorporating the highly varying coefficients into the block preconditioners that we propose. We will see that such considerations can be essential in order to obtain good performance. An important issue is the scalability of the solution methodology. Here, we will study how the convergence of the iterative solver depends on a grid parameter which controls the refinement of the computational mesh. We will see that the novel preconditioners we propose can lead to convergence which is effectively independent of the grid parameter. We also investigate dependence on other model parameters such as the Reynolds number as well as the density and viscosity ratios between the two fluids. Another topic we examine is the use of a multipreconditioned iterative method allowing more than one preconditioner to be used simultaneously. Our results using this approach show some promising features. Finally, we consider an implementation within a more realistic model used in practice for simulating complex airâwater flows. In particular, we will provide results for a problem modelling the breaking of a dam.