Electronic Thesis and Dissertation Repository


Master of Engineering Science


Mechanical and Materials Engineering


J M Floryan


In this work a spectrally accurate algorithm has been developed for the simulation of three-dimensional flows bounded by rough walls. The algorithm is based on the velocity-vorticity formulation and uses the concept of Immersed Boundary Conditions (IBC) for the enforcement of the boundary conditions. The flow domain is immersed inside a fixed computational domain. The geometry of the boundaries is expressed in terms of double Fourier expansions and boundary conditions enter the algorithm in the form of constraints. The spatial discretization uses Fourier expansions in the stream-wise and span-wise directions and Chebyshev expansions in the wall-normal direction. The algorithm can use either the fixed flow rate constraint or the fixed pressure gradient constraint; a direct implementation of the former constraint is described. An efficient solver which takes advantage of the structure of the coefficient matrix has been developed. Taking the advantage of the reality conditions enhances the efficiency of the solver both in terms of memory and computational speed. It is demonstrated that the applicability of the algorithm can be extended to more extreme geometries using the over-determined formulation. Various tests confirm the spectral accuracy of the algorithm.