A Fast Parabolic Module for the Solution of MHD Channel Flow Equations between Electrode Walls

摘要

Two fourth-order methods, based on cubic-splines approximations, are proposed to solve parabolic differential equations. The cubic-splines approximation has a second-order accuracy, which is improved in both methods to fourth-order in different ways. In the first method, the second-order truncation term is estimated by differentiating twice the basic equations. In the other method a local Richardson extrapolation is applied at each marching station to obtain fourth-order accurate values at every two points; subsequent quintic Hermite interpolation is then used to obtain equally accurate values at the remaining points. A von Neumann stability analysis shows that the methods are unconditionally stable. Both methods are applied to a simple boundary-layer problem. The method with local Richardson extrapolation is employed to solve simultaneously the continuity and energy equation describing the behaviour of the electron gas along the cathode wall in an MHD channel. The results indicate that it is worthwhile to reconsider the model of the electrode-plasma interface. (Author)