Title: A primitive variable finite-volume method for incompressible viscous magnetohydrodynamic flows

Authors: Ramesh K. Agarwal

Addresses: Aerospace Engineering, Wichita State University, Wichita, Kansas 67260-0093, USA

Abstract: A recently developed numerical method is employed for computing the numerical solutions of the incompressible Navier-Stokes equations in the presence of a magnetic field. The method is based on the pressure correction approach, but employs a regular grid finite-volume variable arrangement instead of the usual staggered grid arrangement. The pressure equation is derived such that effects which promote the well-known checkerboard instability are not present. A relevant compatibility constraint on pressure is satisfied by Neumann boundary conditions obtained using a vector identity. The transport equations of the magnetic field with solenoidal condition are solved with a similar approach. The unified computational framework is thus developed for the solution of incompressible viscous magnetohydrodynamic flows. Implemented in a second-order-accurate finitevolume code, the algorithm is used to compute the magnetohydrodynamic flow in a pipe. Numerical solution is compared with existing analytical and computational results for various Hartmann numbers.

Keywords: finite volume method; incompressible flow; viscous flow; magnetohydrodynamic flow; MHD flow; magnetic field.

DOI: 10.1504/IJCAT.1998.062195

International Journal of Computer Applications in Technology, 1998 Vol.11 No.3/4/5, pp.170 - 176

Published online: 01 Jun 2014 *

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