Design of CFD code using high level programming paradigms: Free surface flows with arbitrarily moving rigid bodies

OLeg I. Gubanov, M.Sc. Thesis, Memorial University (2007)

Abstract - The objective of this thesis is to design and develop a numerical simulation tool for the class of unsteady free surface flows with arbitrarily moving rigid bodies. The major technical issue encountered in the solution of free surface problems is the appearance of numerical instabilities that arise due to the description of the mesh movement to track the moving boundaries, nonlinearity of the governing equations and boundary conditions implementation at the free surface and rigid body surface.

In the present computational model, fluid flow governed by full Navier-Stokes equations is only modeled within a two-dimensional computational domain. The motion of the air is neglected and the effect of the ambient pressure exerted on the fluid by the air is taken into consideration. The method of solution is based on a finite volume discretization of unsteady Navier-Stokes equations in their pressure-velocity formulation on a fixed Cartesian grid. A special integral form of governing equations is derived by extending the Reynolds transport theorem and then applying it to control volumes containing fluid interface for the first time. The combined volume of fluid and fractional area/volume obstacle representation method, and the cut cell method are employed to track fluid-air and fluid-body interfaces. This combined method is based on techniques used in the commercial fluid dynamics simulation package FLOW-3D developed by Flow Science, Inc. A sparse linear system in pressure and velocity components is solved by using the generalized minimal residual method with incomplete LU preconditioner to advance the simulation of unsteady flow in time.

Creative use of object oriented programming, data abstraction and template metaprogramming paradigms enables us to implement principle computational fluid dynamics concepts, directly, into the computer code developed in the present thesis. This results in a computer program that is easier to understand and maintain. The C++ programming language is chosen as the implementation language since it provides direct support of these modern programming paradigms. Automatic generation of the program code from templates augmented with compile time optimizations and function inlining reduces the size of a manually written code up to four times and meets the high level code efficiency requirements at the Fortran level.

This numerical simulation tool is applied to the problem of unsteady, laminar, two dimensional flow of a viscous incompressible fluid past transversely oscillating circular cylinder in the presence of a free surface. The results of this thesis represent the first comprehensive numerical study conducted on this problem to date. The code validations are presented in special cases and good comparisons with previous experimental and numerical results are obtained.