A discontinuous Galerkin spectral element method compressible flow solver

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Lu, Li

Contributors dc:contributor

• Fischer, Paul F
• Pearlstein, Arne J
• Matalon, Moshe
• Olson, Luke N

• Discontinuous Galerkin, compressible flow solver, high-order

Statement dc:rights

• Copyright 2019 Li Lu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106377

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106377