Solution to Magnetogasdynamics

Abstract

The Riemann problem for a quasilinear hyperbolic system of equations govern-ing the one dimensional unsteady simple wave °ow of an inviscid and perfectly conducting compressible °uid, subjected to a transverse magnetic ¯eld, is solved approximately. This class of equations includes as a special case the Euler equa- tions of gasdynamics. It is noticed that in contrast to the gasdynamic case, the pressure is varying across the contact discontinuity. The iterative procedure is used to ¯nd densities, between left acoustic wave and right contact discontinu-ity, and between right contact discontinuity and right acoustic wave, respectively. All other quantities follow directly throughout the (x; t)-plane, except within rar-efaction waves, where an extra iterative procedure is used along with Gaussian quadrature rule to ¯nd particle velocity; indeed, the determination of the parti- cle velocity involves numerical integration when the magneto-acoustic wave is a rarefaction wave. Lastly, we discuss numerical examples and study the solution in°uenced by the magnetic ¯eld.