SOLUTIONS AND STABILITY ANALYSIS OF BACKWARD-EULER METHOD FOR SIMPLIFIED MAGNETOHYDRODYNAMICS WITH NONLINEAR TIME RELAXATION

Authors : Gamze YÜKSEL, Mustafa Hicret YAMAN

Pages : 45-51

Doi:10.22531/muglajsci.932484

View : 13 | Download : 5

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :In this study, the solutions of Simplified Magnetohyrodynamics insert ignore into journalissuearticles values(SMHD); equations by finite element method are examined with nonlinear time relaxation term. The differential filter κinsert ignore into journalissuearticles values(|u-u ̅ |insert ignore into journalissuearticles values(u-u ̅ );); term is added to SMHD equations. Also SMHD Nonlinear Time Relaxation Model insert ignore into journalissuearticles values(SMHDNTRM); is introduced. The model is discretized by Backward-Euler insert ignore into journalissuearticles values(BE); method to obtain the finite element solutions. Moreover, the stability of the method is proved. The method is found unconditionally stable. The effectiveness of the method is exemplified by several cases with comparing different methods. FreeFem++ is used for all computations.
Keywords : MagnetoHydroDynamics, Backward Euler Method, Nonlinear Time Relaxation, Finite Element Method