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Implicit time integration schemes are widely used in computational fluiddynamics numerical codes to speed-up computations. Indeed, implicit schemesusually allow for less stringent time-step stability constraints than theirexplicit counterpart. The derivation of an implicit scheme is however achallenging and time-consuming task, increasing substantially with the modelequations complexity since this method usually requires a fairly accurateevaluation of the spatial scheme's matrix Jacobian. This article presents aflexible method to overcome the difficulties associated to the computation ofthe derivatives, based on the forward mode of automatic differentiation usingoperator overloading. Flexibility and simplicity of the method are illustratedthrough implicit resolution of various flow models of increasing complexitysuch as the compressible Euler equations, a two-phase flow model in fullequilibrium (Le Martelot, et al., 2014) and a symmetric variant (Saurel , etal., 2003) of the two-phase flow model of (Baer \& Nunziato, 1986) dealing withmixtures in total disequilibrium.

Automatic Differentiation using Operator Overloading (ADOO) for implicit resolution of hyperbolic single phase and two-phase flow models