An exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

“…The MHD flow problem may obtain analytical solution in some special conditions, but it can only be solved numerically in the general situation . In the past several decades, various numerical approximation methods, involving finite element method (FEM) [14][15][16][17][18][19][20][21][22][23], finite difference method (FDM) [7][8][9][10], boundary element method (BEM) [4][5][6], differential quadrature method (DQM) [24], meshfree (meshless) method (MM) [1][2][3], finite volume spectral element method (FVSEM) [25], have been suggested to solve the coupled equations in velocity and magnetic field for the steady magnetohydrodynamic (MHD) duct flow. However, most of them cannot solve the MHD problems with high Ha effectively.…”

“…Tian). a transverse magnetic field with the high Ha, some numerical methods such as finite element and finite difference methods have been developed [7,10,17,19,21,26]. In finite element method, the residual-free bubble functions-based finite element method has drawn researchers' attention [17,19,21,26].…”

“…The upwind difference schemes proposed in [7] are believed that they are not only able to get a reasonable accuracy, but can also resolve high gradients near the layer regions without refining the grid. However, the upwind II scheme proposed in [7] did not seem to be always robust for the solution of the MHD duct flow problems with high Ha (This has been revealed by Problem 1 in Section 5 in [10].) Recently, Li and Tian [10] proposed an exponential highorder compact (EHOC) difference scheme with high accuracy and excellent stability to solve the MHD duct flow problems.…”

“…However, the upwind II scheme proposed in [7] did not seem to be always robust for the solution of the MHD duct flow problems with high Ha (This has been revealed by Problem 1 in Section 5 in [10].) Recently, Li and Tian [10] proposed an exponential highorder compact (EHOC) difference scheme with high accuracy and excellent stability to solve the MHD duct flow problems. The EHOC scheme [10] not only obtained very accurate results at low-tomoderate values of Ha but also computed robustly the MHD duct flow problems at high Ha.…”

“…Recently, Li and Tian [10] proposed an exponential highorder compact (EHOC) difference scheme with high accuracy and excellent stability to solve the MHD duct flow problems. The EHOC scheme [10] not only obtained very accurate results at low-tomoderate values of Ha but also computed robustly the MHD duct flow problems at high Ha. It has been shown in [10] that, compared with the upwind II scheme [7], the EHOC scheme is more effective and robust for the MHD duct flow problems at wide range values of Ha.…”