Abstract:
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.
