Open AccessVirtual element stabilization of convection-diffusion equation with shock capturing
Author(s) -
M. Arrutselvi,
E. Natarajan
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1850/1/012001
Subject(s) - crosswind , shock (circulatory) , discretization , convection–diffusion equation , nonlinear system , galerkin method , petrov–galerkin method , spurious relationship , stability (learning theory) , convection , finite element method , mathematics , mathematical analysis , mechanics , computer science , physics , meteorology , medicine , thermodynamics , statistics , quantum mechanics , machine learning
Streamline upwind Petrov-Galerkin (SUPG) stabilization for the virtual element discretization of the convection-diffusion equation produces local oscillations in the crosswind direction. To overcome such a shortcoming, an additional shock-capturing term is added into the formulation. In this paper, we propose a nonlinear shock-capturing technique and prove the existence and stability of the discrete solution. The resulted nonlinear system of equations is solved using a simple iterative technique. Numerical experiments are conducted to show the efficiency of shock-capturing term in reducing the spurious oscillations along the crosswind direction.