Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme

Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme

Author Moura, R. C. Google Scholar
Silva, A. F. C. Google Scholar
Bigarella, E. D. V. Google Scholar
Fazenda, A. L. Autor UNIFESP Google Scholar
Ortega, M. A. Google Scholar
Abstract This paper proposes two important improvements to shock-capturing strategies using a discontinuous Galerkin scheme, namely, accurate shock identification via finite-time Lyapunov exponent (FTLE) operators and efficient shock treatment through a point-implicit discretization of a PDE-based artificial viscosity technique. The advocated approach is based on the FTLE operator, originally developed in the context of dynamical systems theory to identify certain types of coherent structures in a flow. We propose the application of FTLEs in the detection of shock waves and demonstrate the operator's ability to identify strong and weak shocks equally well. The detection algorithm is coupled with a mesh refinement procedure and applied to transonic and supersonic flows. While the proposed strategy can be used potentially with any numerical method, a high-order discontinuous Galerkin solver is used in this study. In this context, two artificial viscosity approaches are employed to regularize the solution near shocks: an element-wise constant viscosity technique and a PDE-based smooth viscosity model. As the latter approach is more sophisticated and preferable for complex problems, a point-implicit discretization in time is proposed to reduce the extra stiffness introduced by the PDE-based technique, making it more competitive in terms of computational cost. (C) 2016 Elsevier Inc. All rights reserved.
Keywords High-speed flows
Adaptive mesh refinement
Finite-time Lyapunov exponent
Discontinuous Galerkin
High-order methods
Language English
Sponsor FAPESP (Sao Paulo Research Foundation) [2012/16973-5]
Grant number FAPESP:2012/16973-5
Date 2016
Published in Journal Of Computational Physics. San Diego, v. 319, p. 9-27, 2016.
ISSN 0021-9991 (Sherpa/Romeo, impact factor)
Publisher Academic Press Inc Elsevier Science
Extent 9-27
Access rights Closed access
Type Article
Web of Science ID WOS:000377044100002

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