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

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dc.contributor.author Moura, R. C.
dc.contributor.author Silva, A. F. C.
dc.contributor.author Bigarella, E. D. V.
dc.contributor.author Fazenda, A. L. [UNIFESP]
dc.contributor.author Ortega, M. A.
dc.date.accessioned 2019-07-22T15:46:54Z
dc.date.available 2019-07-22T15:46:54Z
dc.date.issued 2016
dc.identifier http://dx.doi.org/10.1016/j.jcp.2016.05.019
dc.identifier.citation Journal Of Computational Physics. San Diego, v. 319, p. 9-27, 2016.
dc.identifier.issn 0021-9991
dc.identifier.uri http://repositorio.unifesp.br/handle/11600/51169
dc.description.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. en
dc.description.sponsorship FAPESP (Sao Paulo Research Foundation) [2012/16973-5]
dc.format.extent 9-27
dc.language.iso eng
dc.publisher Academic Press Inc Elsevier Science
dc.rights Acesso restrito
dc.subject High-speed flows en
dc.subject Adaptive mesh refinement en
dc.subject Finite-time Lyapunov exponent en
dc.subject Discontinuous Galerkin en
dc.subject High-order methods en
dc.title Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme en
dc.type Artigo
dc.description.affiliation ITA, Sao Jose Dos Campos, SP, Brazil
dc.description.affiliation EMBRAER, Commercial Aviat, Sao Jose Dos Campos, SP, Brazil
dc.description.affiliation UNIFESP, Sao Jose Dos Campos, SP, Brazil
dc.description.affiliationUnifesp UNIFESP, Sao Jose Dos Campos, SP, Brazil
dc.description.sponsorshipID FAPESP:2012/16973-5
dc.identifier.doi 10.1016/j.jcp.2016.05.019
dc.description.source Web of Science
dc.identifier.wos WOS:000377044100002



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