AZTEC: A front tracking code based on Godunov's method

Abstract

AZTEC (Adaptive Zoom Tracking—Experimental Code) is a code to solve the one-dimensional gas dynamical equations in a variable area duct with specific implementation for plane, cylindrical, and spherical geometries. The program uses a fixed, locally and adaptively refinable grid, together with a set of moving grid points which migrate through the fixed grid. The moving points represent shocks or contact discontinuities, and they can be created or destroyed, usually as the result of a collision. Mass, energy, and momentum (the last only in the constant area case) are exactly conserved, except after a collision; in that case the conservation error is reduced to invisible levels by spatially localized partial time stepping. The basic difference scheme for both the fixed and moving grid is Godunov's method, with the Riemann solver used to compute both cell boundary fluxes and the speeds of the moving points. Tracking of rarefaction waves on the moving grid is difficult with this method since the waves must be represented as piecewise constant. In one version of AZTEC the rarefaction waves are recorded on the fixed grid with the Lax—Wendroff difference scheme with a small additional viscosity, and most of the numerical experiments have been performed with this version. In another version the polytropic gas equation of state has been replaced by one in which the pressure is a continuous piecewise linear function of specific volume at constant entropy. With this assumption the solution of each Riemann problem is piecewise constant, and our method is exact until the wave structure becomes too complicated. Some preliminary numerical results are exhibited for this version.