THE PIECEWISE-LINEAR PREDICTOR-CORRECTOR CODE - A LAGRANGIAN-REMAP METHOD FOR ASTROPHYSICAL FLOWS

We describe a time-explicit finite-difference algorithm for solving th e nonlinear fluid equations. The method is similar to existing Euleria n schemes in its use of operator-splitting and artificial viscosity, e xcept that we solve the Lagrangian equations of motion with a predicto r-corrector and then remap onto a fixed Eulerian grid. The remap is fo rmulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergenc e tests show that the code has a second-order rate of convergence in s mooth, two-dimensional flow, with pressure forces, gravity, and curvil inear geometry included. While not as accurate on idealized problems a s high-order Riemann-solving schemes, the preditor-corrector Lagrangia n-remap code has great flexibility for application to a variety of ast rophysical problems.