Numerical Analysis of a Finite Element, Crank-nicolson Discretization for Mhd Flows at Small Magnetic Reynolds Numbers
نویسنده
چکیده
We consider the finite element method for time dependent MHD flow at small magnetic Reynolds number. We make a second (and common) simplification in the model by assuming the time scales of the electrical and magnetic components are such that the electrical field responds instantaneously to changes in the fluid motion. This report gives a comprehensive error analysis for both the semi-discrete and a fully discrete approximation. Finally, the effectiveness of the method is illustrated in several numeral experiments.
منابع مشابه
Numerical solution of the one dimensional non-linear Burgers equation using the Adomian decomposition method and the comparison between the modified Local Crank-Nicolson method and the VIM exact solution
The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...
متن کاملNumerical simulation of drop coalescence in the presence of film soluble surfactant
Numerical method is presented for simulation of the deformation, drainage and rupture of axisymmetrical film (gap) between colliding drops in the presence of film soluble surfactants under the influence of van der Waals forces at small capillary and Reynolds numbers and small surfactant concentrations. The mathematical model is based on the lubrication equations in the gap between drops and the...
متن کاملA Posteriori Error Control for Fully Discrete Crank-Nicolson Schemes
We derive residual-based a posteriori error estimates of optimal order for fully discrete approximations for linear parabolic problems. The time discretization uses the Crank– Nicolson method, and the space discretization uses finite element spaces that are allowed to change in time. The main tool in our analysis is the comparison with an appropriate reconstruction of the discrete solution, whi...
متن کاملUncoupling Evolutionary Groundwater-surface Water Flows Using the Crank-nicolson Leapfrog Method
Abstract. Consider an incompressible fluid in a region Ωf flowing both ways across an interface, I, into a porous media domain Ωp saturated with the same fluid. The physical processes in each domain have been well studied and are described by the Stokes equations in the fluid region and the Darcy equations in the porous media region. Taking the interfacial conditions into account produces a sys...
متن کاملA New Linearly Extrapolated Crank-nicolson Time-stepping Scheme for the Nse
We investigate the stability of a fully-implicit, linearly extrapolated Crank-Nicolson (CNLE) time-stepping scheme for finite element spatial discretization of the Navier-Stokes equations. Although presented in 1976 by Baker and applied and analyzed in various contexts since then, all known convergence estimates of CNLE require a time-step restriction. We propose a new linear extrapolation of t...
متن کامل