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Rémi Abgrall, "A review of residual distribution schemes for steady and unsteady compressible fluid dynamics"
In this talk, I will review the current status of the so-called residual distribution schemes applied, in particular, to compressible fluid dynamics problems. Other physical models include the Shallow Water equation and generalization, MHD, etc.This schemes, after the early work of R. Ni at Bombardier, and the seminal work of P.L Roe, in particular his 1981 JCP paper and its extensions to scalar multidimensional schemes, can be considered as finite element methods of the streamline diffusion type. The emphasis is put in non-oscillatory properties, in order to be able to compute flow discontinuities, so that they are non linear by construction. Indeed shock capturing is done in a totally different manner as for stream line diffusion, allowing for a class of parameter free schemes. In a way, the Residual Distribution methods can be seen as a kind of compromise between high order TVD-like finite difference/finite volume schemes and classical finite element methods, in that they borrow ideas from both communities : geometrical flexibility, the residual concept n one side, and non oscillatory, maximum principle on the other one.
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