Highly accurate shock flow calculations with moving grids and mesh refinements, revision 1

Dive one dimensional (1D) and one 2D shock wave problems which propagate obliquely to the coordinate axes are solved by a second order time marching method. It is assumed that the solution region is piecewise continuous, with any discontinuities which may develop being represented by an arctan approximation to a step function. Immediately behind or ahead of a flagged discontinuity, appropriate one side derivatives are used. An explicit moving grid technique is combined with the time integration scheme which yields the correct velocity at discontinuities. Shock fitting is handled automatically and correctly by the choice of the grid velocities. The regularization problem associated with moving grids is handled by a rezoning based on equidistributing the component averaged third derivative. The same second order time integration scheme is used throughout the entire spatial domain.