SUPG-YZ beta computation of chemically reactive convection-dominated nonlinear models

Date

2022-09-01

Author

Cengizci, Suleyman
Uğur, Ömür
Natesan, Srinivasan

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In this computational study, we deal with the stabilized finite element solutions of convection-dominated models having nonlinear reaction mechanisms. The existence of advection terms in these models causes the numerical solutions obtained by standard discretization methods to exhibit nonphysical oscillations. The Galerkin finite element method is stabilized using the Streamline-Upwind/Petrov-Galerkin formulation to avoid such spurious oscillations. The stabilized formulation is also complemented with the YZ beta shock-capturing technique to resolve steep gradients and discontinuities accurately. The nonlinear equation systems arising from the spatial discretizations are solved with the Newton-Raphson method supplemented with the ILU-preconditioned GMRES search technique. The proposed methods are tested on a comprehensive set of nonlinear reactive models. Numerical experiments show that the presented methods and techniques eliminate spurious oscillations significantly and resolve strong gradients accurately. All computations are performed in the FEniCS environment.

Subject Keywords

Finite elements, nonlinear reaction kinetics, SUPG stabilization, YZ beta shock-capturing, convection-dominated, 76M10, 76V05, FINITE-ELEMENT APPROXIMATION, DIFFUSION-REACTION EQUATIONS, INVISCID SUPERSONIC FLOWS, DIMINISHING SOLD METHODS, SPURIOUS OSCILLATIONS, MOVING BOUNDARIES, STABILIZATION, FORMULATIONS, DISSIPATION, ADAPTIVITY

URI

https://hdl.handle.net/11511/100298

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

DOI

https://doi.org/10.1080/00207160.2022.2114794

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

S. Cengizci, Ö. Uğur, and S. Natesan, “SUPG-YZ beta computation of chemically reactive convection-dominated nonlinear models,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100298.