Dilation-based shock capturing for high-order methods

• Published in: International journal for numerical methods in fluids Vol. 82; no. 7; pp. 398 - 416
• Main Authors: Moro, David, Nguyen, Ngoc Cuong, Peraire, Jaime
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 10-11-2016; Wiley Subscription Services, Inc
• Subjects: compressible flow; Computational fluid dynamics; discontinuous Galerkin; Finite element method; Fluids; implicit; Mathematical analysis; Mathematical models; nonlinear solvers; Robustness; Shock capturing; supersonic; transonic; Viscosity
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4223

Summary
In this paper, we introduce a shock‐capturing artificial viscosity technique for high‐order unstructured mesh methods. This artificial viscosity model is based on a non‐dimensional form of the divergence of the velocity. The technique is an extension and improvement of the dilation‐based artificial viscosity methods introduced in Premasuthan et al., and further extended in Nguyen and Peraire . The approach presented has a number attractive properties including non‐dimensional analytical form, sub‐cell resolution, and robustness for complex shock flows on anisotropic meshes. We present extensive numerical results to demonstrate the performance of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.