SUPG-YZβ computation of chemically reactive convection-dominated nonlinear models

Abstract

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 YZβ 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.

Keywords:

• Finite elements
• nonlinear reaction kinetics
• SUPG stabilization
• YZβ shock-capturing
• convection-dominated

AMS 2020 Subject classifications:

• 76M10
• 76V05

Acknowledgments

We would like to express our gratitude to the anonymous reviewers for their thorough and careful reading of the manuscript and valuable suggestions to improve the quality of this work. Prof. T. E. Tezduyar provided insightful comments and fruitful discussions on the stabilization and shock-capturing parameters used in this manuscript, for which we are also grateful.

Disclosure statement

The authors have no conflicts of interest to declare that are relevant to the content of this article.