The Development of a Fully Coupled Solver for the Solution of Free Surface Flows

Abstract

In this thesis, the development of a fully coupled finite volume based free surface flow solver is presented in details. The approach is based on the volume of fluid method (VOF) but extends it to account for a range of couplings, including velocity-pressure, velocity-volume fraction, volume fraction-velocity and volume fraction-pressure couplings. This results in a matrix of coefficients formed at each control volume. Accounting for the various couplings leads to an improved convergence and robustness as compared to segregated type solvers, especially for steady-state applications but also for transient free surface flows. The solver is additionally equipped with a number of techniques, including the treatment of the body forces at the free surface to guarantee a force-balanced solution; this treatment is evaluated analytically and numerically. Also, a very important facet to ensure the geometric constraint is provided in the solver; this is represented by the summation of all volume fractions being enforced to one. In this thesis, a novel implicit approach to enforce this constraint is presented and is compared to standard approaches currently in use. Compressive schemes are also addressed in this work and incorporated in the solver in order to capture the interface with high accuracy and fidelity. The solver also handles turbulence modeling infrastructure for turbulent free surface flows with a set of two- and four-equation models. Worth mentioning is that the performance of the coupled VOF solver is compared to that of a very popular commercial solver which also features a coupled VOF solver. On the other hand, accuracy of the results is evaluated in the light of experimental data along with data generated by the commercial solver. A range of free surface problems exhibiting a variety of boundary conditions and different levels of complexity are attempted. A transient 2D forced sloshing test case is first simulated and the progress of the free surface at a predefined point is monitored in time; it shows consistent results with experimental data. A 3D dam break problem, a very popular free surface testing benchmark, is also simulated; it also produces results comparable to experimental data. Two other steady-state test cases featuring open channel flows past a cylinder and a submerged hydrofoil respectively are simulated. Drag monitors for the two cases show a competitive convergence rate as compared to the commercial software.