Numerical tests of a modified full implicit continuous Eulerian (FICE) scheme with projected normal characteristic boundary conditions for MHD flows

Abstract A numerical method has been developed based on a modified full implicit continuous Eulerian (FICE) scheme and projected normal characteristic boundary conditions for simulating magnetohydrodynamic (MHD) flows which undergo a long process of evolution. An astrophysical flow is chosen for illustration of this procedure, and numerical tests are made to verify the computational stability and physically realistic solution. Three computational tests have been accomplished; they are tests of solving methods, characteristic boundary condition, and time steps. The tests show that the program from the modified FICE scheme with proper boundary conditions and time steps can be made numerically stable for a time long enough to obtain physically plausible solutions.

[1]  Y. Nakagawa.  Evolution of Magnetic Field and Atmospheric Responses - Part Two - Formulation of Proper Boundary Equations , 1981 .

[2]  S. Wu,et al.  A full-implicit-continuous-Eulerian (FICE) scheme for multidimensional transient magnetohydrodynamic (MHD) flows , 1984 .

[3]  S. Wu,et al.  Modeling of energy buildup for a flare-productive region , 1981 .

[4]  W. Werner.  Numerical solution of systems of quasilinear hyperbolic differential equations by means of the method of nebencharacteristics in combination with extrapolation methods , 1968 .

[5]  J. Brackbill,et al.  An implicit, almost-Lagrangian algorithm for magnetohydrodynamics , 1973 .

[6]  S. Wu,et al.  The method of projected characteristics for the evolution of magnetic arches , 1987 .

[7]  R. S. Steinolfson,et al.  Dynamical response of the solar corona. I. Basic formulations , 1976 .

[8]  S. Wu,et al.  Numerical model of a two-dimensional, non-plane transient magnetohydrodynamic flow , 1982 .

[9]  Y. Nakagawa.  Evolution of magnetic field and atmospheric response. I - Three-dimensional formulation by the method of projected characteristics. II - Formulation of proper boundary equations. [stellar magnetohydrodynamics] , 1981 .

[10]  Y. Nakagawa.  Evolution of solar magnetic fields - A new approach to MHD initial-boundary value problems by the method of nearcharacteristics , 1980 .

[11]  G. W. Hedstrom,et al.  Nonreflecting Boundary Conditions for Nonlinear Hyperbolic Systems , 1979 .

[12]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[13]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[14]  Y. Shin,et al.  Two-dimensional fluid-transient analysis by the method of nearcharacteristics , 1978 .

[15]  A. A. Amsden,et al.  A numerical fluid dynamics calculation method for all flow speeds , 1971 .

[16]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.