Work

An extended discontinuous Galerkin shock tracking method

Year: 2024

Type: article

Abstract: In this paper, we introduce a novel high‐order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso‐contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two‐dimensional problems, progressively increasing in complexity.

Source: International Journal for Numerical Methods in Fluids

DOI: 10.1002/fld.5293

Authors: Jakob Vandergrift, Florian Kummer

Institution: Technische Universität Darmstadt

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,220

Funder: Technische Universität Darmstadt