Date of Award


Degree Type


Degree Name

Master of Engineering Science


Mechanical and Materials Engineering


J.M. Floryan


A grid-less, folly-implicit, spectrally accurate algorithm for solving three-dimensional, stationary and time dependent heat conduction problems in the presence of fixed as well as moving boundaries has been developed. The algorithm is based on the concept of immersed boundary conditions (IBC), where the physical domain is immersed within the computational domain and the boundary conditions take the form of internal constraints. The IBC method avoids the need to construct adaptive, time-dependent grids resulting in the reduction of the required computational resources while, at the same time, maintaining a sharp resolution of the location of the boundaries. The algorithm is spectrally accurate in space and capable of delivering first-, second-, third- and fourth- order accuracy in time. Given a potentially large size of the resultant linear algebraic system, various methods that take advantage of the special structure of the coefficient matrix have been explored in search for an efficient solver, including a specialized direct solver as well as serial and parallel iterative solvers. The specialized direct solver has been found to be the most efficient from the points of view of speed of the computations and memory requirements.



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