A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction–convection–diffusion equations

Date

2023-07-01

Author

Cengizci, Süleyman
Uğur, Ömür
Natesan, Srinivasan

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In this computational study, stabilized finite element solutions of convection-dominated stationary and linear reaction–convection–diffusion equations are studied. Although the standard (Bubnov–) Galerkin finite element method (GFEM) is one of the most robust, efficient, and reliable methods for solving many engineering problems and scientific computations, it typically suffers from numerical instabilities when solving convection-dominated problems. Towards that end, this work deals with a stabilized version of the standard GFEM, called the streamline-upwind/Petrov–Galerkin (SUPG) formulation, to overcome the instability issues arising when solving such problems. The SUPG-stabilized formulation is further supplemented with a shock-capturing mechanism, called YZ β shock-capturing, to provide additional stability around steep gradients. A comprehensive set of test examples is provided to assess and compare the performances of the proposed methods, i.e., the GFEM, SUPG, and SUPG-YZ β . It is observed that the GFEM approximations involve spurious oscillations for small values of the diffusion parameter, as expected. We observe through numerical experiments that such globally spread oscillations are suppressed significantly when the SUPG formulation is employed. It is also demonstrated that the SUPG-stabilized formulation needs additional stability to resolve localized sharp layers, and the SUPG-YZ β formulation yields better shock resolutions for such regions.

Subject Keywords

Boundary layer, Convection-dominated differential equations, Finite elements, Interior layer, Shock-capturing

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85163633278&origin=inward
https://hdl.handle.net/11511/104609

Journal

Computational and Applied Mathematics

DOI

https://doi.org/10.1007/s40314-023-02370-2

Collections

Graduate School of Applied Mathematics, Article

Citation Formats

S. Cengizci, Ö. Uğur, and S. Natesan, “A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction–convection–diffusion equations,” Computational and Applied Mathematics, vol. 42, no. 5, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85163633278&origin=inward.