Implicit-explicit hybrid method for Lagrangian hydrodynamics

We describe a new implicit-explicit hybrid method for solving the equations of hydrodynamics. The scheme is an extension of the explicit second-order piecewise-parabolic method (PPM) which is unconditionally stable. The scheme is thus of the Godunov type. It is conservative, accurate to second order in both space and time, and makes use of a nonlinear Riemann solver to obtain fluxes of the conserved quantities. The hybrid character of the method provides increased accuracy and computational efficiency. Switching between implicit and explicit formulations occurs smoothly and in a natural way and is performed separately for each characteristic family of waves. The method provides high resolution with shocks spread over only one zone and can produce accurate answers to most reasonable problems without the use of an artificial viscosity