| Full text | |
| Author(s): |
Moura, R. C.
[1]
;
Silva, A. F. C.
[1]
;
Bigarella, E. D. V.
[2]
;
Fazenda, A. L.
[3]
;
Ortega, M. A.
[1]
Total Authors: 5
|
| Affiliation: | [1] ITA, Sao Jose Dos Campos, SP - Brazil
[2] EMBRAER, Commercial Aviat, Sao Jose Dos Campos, SP - Brazil
[3] UNIFESP, Sao Jose Dos Campos, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Journal of Computational Physics; v. 319, p. 9-27, AUG 15 2016. |
| Web of Science Citations: | 2 |
| 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. (AU) | |
| FAPESP's process: | 12/16973-5 - The usage of Discontinuous Galerkin spectral techniques in the numerical simulation of complex problems in fluid dynamics |
| Grantee: | Marcos Aurélio Ortega |
| Support Opportunities: | Regular Research Grants |