Element centered smooth artificial viscosity in discontinuous Galerkin method for propagation of acoustic shock waves on unstructured meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:366

Article

Tripathi, Bharat B.¹  Luca, Adrian¹  Baskar, Sambandam²  Coulouvrat, Francois¹  Marchiano, Regis¹ 

[1] Sorbonne Univ, CNRS, Inst Jean Le Rond dAlembert, 4 Pl Jussieu, F-75005 Paris, France

[2] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

关键词: Discontinuous Galerkin;    Shock capturing;    Artificial viscosity;    Nonlinear acoustics;   

DOI  :  10.1016/j.jcp.2018.04.010

来源: Elsevier

【 摘 要 】

This work aims at developing a high-order numerical method for the propagation of acoustic shock waves using the discontinuous Galerkin method. High order methods tend to amplify the formation of spurious oscillations (Gibbs phenomenon) around the discontinuities/shocks, associated to the relative importance of higher-harmonics resulting from nonlinear propagation (in our case). To handle this critical issue, a new shock sensor is introduced for the sub-cell shock capturing. Thereafter, an element-centered smooth artificial viscosity is introduced into the system wherever an acoustic shock wave is sensed. Validation tests in 1D and 2D configurations show that the method is well-suited for the propagation of acoustic shock waves along with other physical effects like geometrical spreading and diffraction. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free