Alternating direction implicit numerical solution of the time-dependent, three-dimensional, resistive, single fluid magnetohydrodynamic equations

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1980

OSTI ID:5526550

Finan, III, C H

Resistive magnetoyhydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are solved simultaneously to avoid synchronization errors. While the continuity and magnetic flux equations are expressed as conservation laws, the momentum and energy equations are nonconservative. This is to: (1) provide enhanced numerical stability by eliminating errors introduced by the nonvanishing of ..delta...B on the finite difference mesh; and, (2) allow the simulation of low beta plasmas. To allow for general simulations, the boundary conditions may be Dirichlet, Neumann, or periodic. A conservation boundary condition based on the physical properties of the wall is presented. The resulting finite difference equations are a coupled system of nonlinear algebraic equations which are solved by the Newton-Raphson iteration technique. The model is applied to a number of problems of importance in magnetic fusion research. Ideal and resistive internal kink instabilities are simulated in a Cartesian geometry. Growth rates and nonlinear saturation amplitudes are found to be in agreement with previous analytic and numerical predictions. These instabilities are simulated in square cross section torus.

• Research Organization: California Univ., Davis (USA)
• OSTI ID: 5526550
• Country of Publication: United States
• Language: English

Related Subjects

640430* -- Fluid Physics-- Magnetohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
COMPUTER CALCULATIONS
COORDINATES
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
ITERATIVE METHODS
KINK INSTABILITY
MAGNETOHYDRODYNAMICS
MATHEMATICAL MODELS
MECHANICS
MESH GENERATION
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PINCH EFFECT
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
REVERSE-FIELD PINCH
THREE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE