A Spacetime Discontinuous Galerkin Method for Hyperbolic Conservation Laws

The basic SDG approximation is a simple Bubnov-Galerkin projection that is not prone to global patterns of spurious oscillations. However, it does require stabilization to eliminate local overshoot and undershoot in the immediate vicinity of shocks and other discontinuous solution features. We address this requirement with a diffusion operator whose intensity is controlled by a shock indicator that measures the relative strength of the high-frequency components of the SDG approximation. Results demonstrating the performance of the SDG method, the h-adaptive refinement scheme, and the diffusion operator for applications of the inviscid Euler equations in one and two spatial dimensions are presented.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical and Applied Mechanics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Palaniappan, Jayandran

Contributors dc:contributor

• Haber, Robert B.

• Engineering, Mechanical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3269996

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87741