Date of Award
2018
Document Type
Open Access Dissertation
Degree Name
Doctor of Philosophy in Mathematical Sciences (PhD)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Alexander E. Labovsky
Committee Member 1
Allan A. Struthers
Committee Member 2
Jiguang Sun
Committee Member 3
Aleksandr V. Sergeyev
Abstract
This dissertation contains several approaches to resolve irregularity issues of CFD problems, including a decoupling of non-linearly coupled fluid-fluid interaction, due to high Reynolds number. New models present not only regularize the linear systems but also produce high accurate solutions both in space and time. To achieve this goal, methods solve a computationally attractive artificial viscosity approximation of the target problem, and then utilize a correction approach to make it high order accurate. This way, they all allow the usage of legacy code | a frequent requirement in the simulation of fluid flows in complex geometries. In addition, they all pave the way for parallelization of the correction step, which roughly halves the computational time for each method, i.e. solves at about the same time that is required for DNS with artificial viscosity. Also, methods present do not requires all over function evaluations as one can store them, and reuse for the correction steps. All of the chapters in this dissertation are self-contained, and introduce model first, and then present both theoretical and computational findings of the corresponding method.
Recommended Citation
Aggul, Mustafa, "HIGH ACCURACY METHODS AND REGULARIZATION TECHNIQUES FOR FLUID FLOWS AND FLUID-FLUID INTERACTION", Open Access Dissertation, Michigan Technological University, 2018.
Included in
Fluid Dynamics Commons, Numerical Analysis and Computation Commons, Partial Differential Equations Commons