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

dc.contributor.authorMoura, R. C.
dc.contributor.authorSilva, A. F. C.
dc.contributor.authorBigarella, E. D. V.
dc.contributor.authorFazenda, A. L. [UNIFESP]
dc.contributor.authorOrtega, M. A.
dc.description.abstractThis 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.en
dc.description.affiliationITA, Sao Jose Dos Campos, SP, Brazil
dc.description.affiliationEMBRAER, Commercial Aviat, Sao Jose Dos Campos, SP, Brazil
dc.description.affiliationUNIFESP, Sao Jose Dos Campos, SP, Brazil
dc.description.affiliationUnifespUNIFESP, Sao Jose Dos Campos, SP, Brazil
dc.description.sourceWeb of Science
dc.description.sponsorshipFAPESP (Sao Paulo Research Foundation) [2012/16973-5]
dc.identifier.citationJournal Of Computational Physics. San Diego, v. 319, p. 9-27, 2016.
dc.publisherAcademic Press Inc Elsevier Science
dc.rightsAcesso restrito
dc.subjectHigh-speed flowsen
dc.subjectAdaptive mesh refinementen
dc.subjectFinite-time Lyapunov exponenten
dc.subjectDiscontinuous Galerkinen
dc.subjectHigh-order methodsen
dc.titleLyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin schemeen