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Time-implicit hydrodynamics for Euler flows. (English. French summary) Zbl 1334.76095
Summary: We consider the Euler equations with gravity source terms, and derive a time-implicit resolution scheme from the explicit one developed by the third author et al. [“A Godunov-type solver for the numerical approximation of gravitational flows”, Commun. Comput. Phys. 15, No. 1, 46–75 (2014; doi:10.4208/cicp.060712.210313a)]. 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.
MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q31 Euler equations
Software:
HERACLES; PETSc; TAPENADE
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