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Title:A discontinuous Galerkin spectral element method compressible flow solver
Author(s):Lu, Li
Director of Research:Fischer, Paul F
Doctoral Committee Chair(s):Fischer, Paul F
Doctoral Committee Member(s):Pearlstein, Arne J; Matalon, Moshe; Olson, Luke N
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Discontinuous Galerkin, compressible flow solver, high-order
Abstract:We develop and implement algorithms for highly-scalable high-order compressible flow simulation using the discontinuous Galerkin spectral element method. The algorithms are designed for simulation of compressible turbulence in realistic engineering geometries that are relevant to a broad range of mechanical engineering applications. Such problems are difficult because of high computational costs and stringent requirements for accurate integration over a wide range of space- and time-scales. Features of this solver include exponential spatial convergence, fast matrix-free operator evaluation, implicit time-stepping schemes, highly-scalable iterative solvers, effective stabilization techniques, and moving-mesh capabilities. Novel nonlinear filter-based artificial viscosity methods have been developed for effective regularization of challenging scalar transport problems in high-order methods and have found application in shock-capturing for the compressible flow solver. Moving-mesh capabilities via the arbitrary Lagrangian-Eulerian method are verified and have enabled simulation of complex engineering applications with moving geometries such as flows in internal combustion engines. Spatial (exponential) and temporal (up to fourth-order) convergence rates of the underlying numerical methods are established. Scalability of the solver, up to realizable strong-scale limits, establishes that the code is suitable for large-scale parallel computing applications. Several proposed preconditioning strategies are evaluated. The solver is demonstrated on a variety of flow problems, such as nearly-incompressible flows, supersonic flows, high Reynolds number flows, shock problems, and moving-geometry problems.
Issue Date:2019-12-05
Type:Text
URI:http://hdl.handle.net/2142/106377
Rights Information:Copyright 2019 Li Lu
Date Available in IDEALS:2020-03-02
Date Deposited:2019-12


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