Date of Award


Degree Type


Degree Name

Master of Engineering Science


Mechanical and Materials Engineering


Dr. Jerzy M. Floryan


The objective of this work is to develop a spectrally-accurate algorithm for simulations of three-dimensional flows in domains bounded by rough boundaries. The proposed algorithm relies on the velocity-vorticity formulation and uses the Immersed Boundary Conditions concept for the enforcement of the flow boundary conditions. Discretization relies on the Fourier expansions in the two periodic directions and Chebyshev expansion in the transverse direction. The algebraic equations are constructed using Galerkin projection method. The boundary conditions have been implemented using a Tau-like procedure where the boundary relations have been constructed on the basis of the Immersed Boundary Conditions concept. Special solvers that take advantage of the structure of the relevant coefficient matrix have been developed. Various tests have been performed in order to illustrate the performance of the algorithm. It is verified that in the limiting cases where alternative solutions are available the error of the solution can be reduced to machine level with a reasonable computational effort.



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