A Detached Shock Calculation by Second Order Finite Differences Classic Reprint

Excerpt from A Detached Shock Calculation by Second Order Finite Differences

A detached shock problem for a symmetric curved convex cylindrical body moving parallel to its plane of symmetry was solved using a third order accurate Richtmyer form of the lax-wendroff conservation equations. One innovation is an easy to use artificial viscosity term which preserves the high order of accuracy of the calcula tion while removing the non-linear instabilities which otherwise appear in the shock region and near boundaries. Another innovation is a simple transformation of Cartesian space which changes the curved body into a straight line, thus reducing the large number of special points and irregularly shaped mesh regions which would otherwise appear in the difference method calculation. Such trans formations are shown to preserve the conservation property of the system of differential equations. Other aspects of the third order artificial viscosity term and the trans formation are discussed. The results of a numerical.

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