Application of the Hybridized Discontinuous Galerkin Method for Solving One-Dimensional Coupled Burgers Equations
Year: 2024
Type: article
Abstract: This paper is devoted to proposing hybridized discontinuous Galerkin (HDG) approximations for solving a system of coupled Burgers equations (CBE) in a closed interval. The noncomplete discretized HDG method is designed for a nonlinear weak form of one-dimensional $x-$variable such that numerical fluxes are defined properly, stabilization parameters are applied, and broken Sobolev approximation spaces are exploited in this scheme. Having necessary conditions on the stabilization parameters, it is proven in a theorem and corollary that the proposed method is stable with imposed homogeneous Dirichlet and/or periodic boundary conditions to CBE. The desired HDG method is stated by using the Crank-Nicolson method for time-variable discretization and the Newton-Raphson method for solving nonlinear systems. Numerical experiences show that the optimal rate of convergence is gained for approximate solutions and their first derivatives.
Authors: Shima Baharloui, Nabi Chegini, Reza Mokhtari
Institutions: Isfahan University of Technology, Tafresh University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6888675638
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