Time multigrid methods and D-adaptivity for coupled fluid flow solvers

This Thesis is about the application of coupled multigrid solvers to the numeri- cal simulation of viscous incompressible fluids. In the centre of discussion is the adaptivity between a one-dimensional solver and a two-dimensional one. The methodology used has proved highly successful for single-and multi-phase laminar flows, leading to solution algorithms that are robust, efficient and accu- rate. The solvers presented here required a considerable number of algorithmic developments. Some of them have demanded the use of some well-known software packages. The Thesis outline is as follows: firstly, the modelling of transient single-phase and multi-phase flows is reviewed, together with a brief overview of the numerical schemes and multigrid methods used in the solvers. Secondly, the Navier-Stokes governing equations are presented and the space discretization formulas based on a control volume are formulated. After having specified the solution algorithms we present results for each solver for a set of test cases of varying complexity. Com- parison with our reference commercial code is outlined, showing good agreement in the results. Interpolation transfer operators used in the interface between the one-dimensional solver and the two-dimensional one are addressed. The coupled solvers are then applied on the numerical simulation of the transient flows on two complex multi- domain problems. Comparison results with the two-dimensional solvers have been performed. The question of performance and accuracy is addressed in detail, both in terms of robustness and speed of convergence. Good accelerations are obtained using the coupled solver. The CPU-time spent to reach the expected steady-state solution is about ten to thirty five percent of the equivalent two-dimensional solver. Considerable gains in memory usage have been achieved. The robustness has been easily verified in the comparison process with the two-dimensional transient solvers. Analytic solutions have been formulated and discussed. However some dependence on the Reynolds numbers has been observed. This was due to the geometric constraints of the complex test cases and the change of some fluid properties.