In this paper we propose an asymptotic preserving scheme for a family of Friedrichs systems on unstructured meshes based on a decomposition between the hyperbolic heat equation and a linear hyperbolic which not involved in the diffusive regime. For the hyperbolic heat equation we use asymptotic preserving schemes recently designed in [FHSN11]-[BDF11]. To discretize the second part we use classi...

In this paper I review three key topics in CFD that have kept researchers busy for half a century. First, the concept of upwind differencing, evident for 1-D linear advection. Second, its implementation for nonlinear systems in the form of highresolution schemes, now regarded as classical. Third, its genuinely multidimensional implementation in the form of residual-distribution schemes, the mos...

This paper investigates the performances of approximate Riemann solvers (ARSs) for hyperbolic traffic models from family generic second-order flow modeling. Three are selected, including HLL, HLLC, and Rusanov solvers, evaluated comprehensively against model by Zhang (2002) a variant phase-transition Colombo with continuous solution domain. The ARSs investigated using extensive numerical tests,...

In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally 1 contracting and TVD. However, the Caputo derivative leads to the modified CFL-type stability condition, ( t) = O( x...

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good...

In this paper, we propose monotonicity preserving and total variation diminishing (TVD) multigrid methods for solving scalar conservation laws. We generalize the upwind-biased residual restriction and interpolation operators for solving linear wave equations to nonlinear conservation laws. The idea is to define nonlinear restriction and interpolation based on localRiemann solutions. Theoretical...

We study the stability of some finite difference schemes for symmetric hyperbolic systems in two space dimensions. For the so-called upwind scheme and the Lax-Wendroff scheme with a stabilizer, we show that stability is equivalent to strong stability, meaning that both schemes are either unstable or `-decreasing. These results improve on a series of partial results on strong stability. We also ...

We develop a second-order central-upwind scheme for the non-hydrostatic version of the Saint-Venant system recently proposed in [M.-O. Bristeau and J. Sainte-Marie, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), pp. 733–759]. The designed scheme is both well-balanced (capable of exactly preserving the “lake-at-rest” steady state) and positivity preserving. We then use the central-upwind scheme ...