Analytical solution of converging shock wave in magnetogasdynamics

Abstract

In this paper, a similarity solution to a problem in magnetogasdynamics with strong converging cylindrical shock wave is examined. An analytical description of converging shock waves is presented by replacing the previous approach for numerical solutions of the ordinary differential equations with a theoretical study of the singular points of the differential equations. A study of singular points of the system of differential equations leads to an analytic description of the flowfield and a determination of the similarity exponent. The influences of adiabatic heat exponent and magnetic field strength on the flow pattern for various cases are assessed. The general behavior of the velocity and density distribution remains unaffected. However, the pressure profiles are greatly affected by the magnetic field interaction. Copyright ©2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.