Author(s): D. Zugliani; G. Rosatti
Keywords: No keywords
Abstract: The Osher solver (Osher&Solomon 1982) is a well-known numerical approach to estimate solutions of Riemann problems deriving from the finite volume method with Godunov fluxes applied to hyperbolic systems of Partial Differential Equations (PDEs). Recently, in Dumbser&Toro (2011b), the applicability of the solver has been extended to purely nonconservative systems. Nevertheless, shallow flows are described by a system where both conservative and non-conservative terms are present simultaneously. Some effort must be done to use the solver in this joined situation. In this work, we combined the conservative and non-conservative formulation ending up with a simple but powerful extension of the Osher solver suitable for the Shallow Water (SW) partially nonconservative PDEs systems. We also introduced a linear path in terms of primitive variables, instead of conserved ones. This approach reduces a little bit the computational cost in cases with simple linear relations between conserved and primitive variables (fixed-bed flows), while the cost reduction becomes more important when the relation is highly nonlinerar (mobile-bed flows) and the Jacobian of the fluxes can be expressed only in term of primitive variables. Finally, we exploited the possibility to use an explicit expression of the path integral of the non-conservative terms instead of a numerical approximation of it, e.g. the work of Rosatti&Begnudelli (2010).