A Two Level Discretization Method for the Mhd Equations
نویسندگان
چکیده
In this paper we describe and analyze a two-level method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. The MHD equations model the ow of a viscous, incompressible, electrically conducting uid, interacting with magnetic and electric elds. These arise in plasma physics, nuclear reactor technology, and geophysics. The suggested algorithm involves solving a small nonlinear problem on a coarse mesh and then one large linear system on a ne mesh.
منابع مشابه
A Two-level Discretization Method for the Stationary Mhd Equations∗
We describe and analyze a two-level finite-element method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics (or MHD). These equations, which model the flow of electrically conducting fluids in the presence of electromagnetic fields, arise in plasma physics and liquid-metal technology as well as in geophysics and astronomy. We treat the equations under ph...
متن کاملUnconditional stability of a partitioned IMEX method for magnetohydrodynamic flows
Magnetohydrodynamic (MHD) flows are governed by Navier–Stokes equations coupled with Maxwell equations through coupling terms. We prove the unconditional stability of a partitioned method for the evolutionary full MHD equations, at high magnetic Reynolds number, written in the Elsässer variables. The method we analyze is a first-order onestep scheme, which consists of implicit discretization of...
متن کاملHigh Accuracy Method for Magnetohydrodynamics System in Elsässer Variables
The MHD flows are governed by the Navier-Stokes equations coupled with the Maxwell equations through coupling terms. We prove the unconditional stability of a partitioned method for the evolutionary full MHD equations, at high magnetic Reynolds number, in the Elsässer variables. The method we propose is a defect correction second order scheme, and entails the implicit discretization of the subp...
متن کاملUnstaggered constrained transport methods for ideal magnetohydrodynamic equations
The ideal magnetohydrohynamic (MHD) equations are important in modeling different phenomena in a wide range of plasma physical applications. This thesis focuses on the development of finite volume methods for numerical solutions of the ideal MHD equations on Cartesian, logically rectangular, and hexahedral mapped grids. One major challenge in numerically solving the MHD equations in more than o...
متن کاملNested Iteration and First-Order System Least Squares for Incompressible, Resistive Magnetohydrodynamics
This paper develops a nested iteration algorithm to solve time-dependent nonlinear systems of partial differential equations. For each time step, Newton’s method is used to form approximate solutions from a sequence of nested spaces, where the resolution of the approximations increases as the algorithm progresses. Nested iteration results in most of the iterations being performed on coarser gri...
متن کامل