Time-Implicit Hydrodynamics for Euler Flows

We consider the Euler equations with gravity source terms, and derive a time-implicit resolution scheme from the explicit one developed by Vides et al. [8]. This requires computing a Jacobian matrix, which is done symbolically using the automatic differentiation tool TAPENADE developed at Inria. The resulting sparse linear system is solved using the PETSc library. We present parallel numerical results for a 2-D Rayleigh-Taylor instability on up to 4096 CPU cores.