Utilizing time-reversibility for shock capturing in nonlinear hyperbolic conservation laws. (30th October 2022)

• Record Type: Journal Article
• Authors: Dzanic, T.; Trojak, W.; Witherden, F.D.
• Is Part Of: Computers & fluids. Volume 247(2022)
• Publication Date: 2022-10-30
• Subjects: Shock capturing -- Artificial viscosity -- Hyperbolic systems -- Euler equations -- Ideal magnetohydrodynamics -- Spectral element method; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2022.105652
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time in the vicinity of shocks. The proposed approach does not require any additional governing equations or a priori knowledge of the hyperbolic system in question, is independent of the mesh and approximation order, and requires the use of only one tunable parameter. The primary novelty is that the resulting artificial viscosity is unique for each component of the conservation law which is advantageous for systems in which some components exhibit discontinuities while others do not. The efficacy of the method is shown in numerical experiments of multi-dimensional hyperbolic conservation laws such as nonlinear transport, Euler equations, and ideal magnetohydrodynamics using a high-order discontinuous spectral element method on unstructured grids. Highlights: Time-reversibility of hyperbolic conservation laws explored for shock capturing. Vector-valued artificial viscosity formed through reversibility metric. Sub-element resolution of shocks using very high order spectral element methods.