Author(s): Lorenzo Begnudelli; Giorgio Rosatti
Linked Author(s): Giorgio Rosatti
Keywords: No Keywords
Abstract: In this paper we present a novel general formulation of the Generalized Roe solver for hyper-concentrated 1D shallow flows over a mobile bed. Hyper-concentrated flows are mathematically defined by a hyperbolic system of three partial differential equations. The system shows non-conservative terms, is highly nonlinear, and its whole structure depends on the closure relationship used to define the concentration. In earlier works, a well-balanced Generalized Roe solver has been derived for 1D and 2D flows. In these approaches, the solution of the Riemann Problem (RP) is obtained from the exact solution of a locally linearized problem, by writing a Jacobian matrix of the system as a function of proper averages of the primitive variables. The formulation of the scheme is not unique and depends on the adopted set of averages. Based on the closure, not only different formulations of the solver are obtained, but more in general the derivation can be quite easy or extremely complicated. In any case, so far only Roe schemes relative to specific closures have been derived. In this paper, we write a general formulation of the Roe scheme, valid for any possible closure. In fact, we treat the concentration as a function of the other variables and write the Jacobian in terms of its partial derivatives. The method is completely general, easy to implement, and as accurate as the standard Roe approach.
Year: 2012