Stabilizing subgrid FEM solution of the natural convection flow under high magnitude magnetic field on sinusoidal corrugated enclosure

ABSTRACT

This study deals with the stabilized finite element solution of the steady, natural convection flow in an enclosure under a magnetic field applied perpendicular to the sinusoidal corrugated vertical walls of the enclosure, in terms of primitive variables. Several vertical sinusoidal functions are selected for the comparison. A stabilized FEM scheme called SSM is proposed in order to obtain a stable solution for the high values of problem parameters with a cheap computational cost. Proposed numerical scheme with linear elements is tested with the other well-known stabilization method called SUPG and also with the higher order element combinations ($Q_2-Q_1$). Obtained solutions show a better accuracy of SSM compared to SUPG in terms of the $L_2$ norm and also show the well-known characteristics of the natural convection MHD flow. The decrease in the convection heat transfer with an increase in the size of the heat source placed in the bottom wall is observed.

KEYWORDS:

• Stabilizing subgrid
• natural convection
• MHD
• FEM

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 76E25
• 80M10

Disclosure statement

No potential conflict of interest was reported by the authors.