A full-implicit-continuous-Eulerian (FICE) scheme for multidimensional transient magnetohydrodynamic (MHD) flows

• Published in: Journal of computational physics Vol. 55; no. 1; pp. 33 - 64
• Main Authors: Hu, Y.Q, Wu, S.T
• Format: Journal Article
• Language: English
• Published: Legacy CDMS Elsevier Inc 01.07.1984; Elsevier
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Magnetohydrodynamics and electrohydrodynamics; Physics; Plasma Physics; Transient flow; MHD flow; Calculating method; Finite difference method
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/0021-9991(84)90014-7

A full-implicit-continuous-Eulerian (FICE) scheme is developed for solving multidimensional transient magnetohydrodynamic (MHD) flow problems. The resulting difference equations are solved through a single-loop iteration in which the time-advanced pressure equation is solved by using the line-by-line iteration method (Patankar, “Numerical Heat Flow,” Hemisphere, Washington, D.C., 1980). In order to keep the boundary conditions self-consistent, a new formulation of boundary conditions is developed for this two-dimensional initial boundary value magnetohydrodynamic (MHD) flow problem. The merit of this new formulation is that improved consistency and accuracy on both physical and computational boundary values are obtained when compared to earlier methods. The stipulation of the boundary conditions is based on the projected characteristic method. The boundaries in a numerical computation may be classified into the following two categories: (i) Physical boundaries, on which the number of dependent variables are to be arbitrarily specified, would be limited to the number of incoming characteristics that are projected in the n - t plane, where n is the unit normal of the boundary in question and t is time. The rest of the variables (if any) should satisfy the compatibility equations along the outgoing projected characteristics in the n - t plane. (ii) Computational boundaries, on which a related set of compatibility equations should also be satisfied. In addition, a new nonreflecting boundary condition is introduced by taking all the spatial derivative terms of dependent variables to be zero in the characteristic equations along the incoming projected characteristics in the n - t plane. A numerical example for an astrophysical fluid is given to illustrate the present algorithm and boundary conditions. In addition, the comparison between the results of using the present nonreflecting boundary condition and the two conventional ones (i.e., equivalue and linear extrapolations) is made. It shows that the nonreflecting boundary condition formulated in this paper gives much smaller (almost null) reflection after the disturbance has reached the boundary and, therefore, can provide more accurate numerical results.