Conferenciante: Manuel J. Castro Díaz (Universidad de Málaga)
Título: "Approximate Osher-Solomon Schemes for hyperbolic systems"
Fecha y hora: Jueves 20 de abril de 2017, 13:10
Lugar de encuentro: Seminario de la primera planta, IEMath-GR
This talk is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver (see [Osher-Solomon 1982]), and extend in some sense the schemes proposed in [Dumbser-Toro 2011]. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions (see Castro-Gallardo-Marquina 2014). The schemes have been tested with different initial value Riemann problems for ideal gas dynamics, magnetohydrodynamics and multilayer shallow water equations. The numerical tests indicate that the proposed schemes are robust, stable and accurate with a satisfactory time step restriction, and provide an efficient alternative for approximating time-dependent solutions in which the spectral decomposition is computationally expensive.