BibTeX
@ARTICLE{
         Fraysse2019Adu,
       title = "Automatic differentiation using operator overloading ({ADOO}) for implicit resolution
         of hyperbolic single phase and two-phase flow models",
       journal = "Journal of Computational Physics",
       volume = "399",
       pages = "108942",
       year = "2019",
       issn = "0021-9991",
       doi = "10.1016/j.jcp.2019.108942",
       url = "https://doi.org/10.1016/j.jcp.2019.108942",
       author = "Fran\c{c}ois Fraysse and Richard Saurel",
       keywords = "Automatic differentiation, Implicit, Two-phase, Finite volume, Unstructured
         meshes",
       abstract = "Implicit time integration schemes are widely used in computational fluid dynamics
         to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step
         stability constraints than their explicit counterpart. The derivation of an implicit scheme is
         however a challenging and time-consuming task, increasing substantially with the model equations
         complexity since this method usually requires fairly accurate evaluation of the spatial
         scheme's matrix Jacobian. This article presents a flexible method to overcome the difficulties
         associated to the computation of the derivatives, based on the forward mode of automatic
         differentiation using operator overloading (ADOO). Flexibility and simplicity of the method are
         illustrated through implicit resolution of various flow models of increasing complexity such as the
         compressible Euler equations, a two-phase flow model in full equilibrium [28] and a symmetric
         variant [44] of the two-phase flow model of Baer and Nunziato [2] dealing with mixtures in total
         disequilibrium.",
       ad_area = "Computational Fluid Dynamics"
}