Jump conditions for shock waves on the surface of a star

• DOI: 10.1007/s10509-008-9949-6
• Publication Date: 2008-11-26T18:28:00Z
• Authors: Roy S. Baty; Don H. Tucker
• Keywords: Heaviside step function; Classification of discontinuities; Hydraulic jump; Dirac delta function

This article applies nonstandard analysis to derive jump conditions for one-dimensional, diverging, magnetogasdynamic shock waves emerging on the surface of a star. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions for the flow parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters. It is shown here that the equations modeling a family of magnetogasdynamic shock waves yield products of generalized functions that may be analyzed consistently using nonstandard predistributions.