The Osher-Chakrabarthy family of linear flux-modification schemes is considered. Improved lower bounds on the compression factors are provided, which suggest the viability of using the unlimited version. The LLF flux formula is combined with these schemes in order to obtain compact finite-difference algorithms. The resulting schemes are applied to a battery of numerical tests, going from advect...

This article analyses the convergence of the Vertex Approximate Gradient (VAG) scheme recently introduced in Eymard et al. 2012 for the discretization of multiphase Darcy flows on general polyhedral meshes. The convergence of the scheme to a weak solution is shown in the particular case of an incompressible immiscible two-phase Darcy flow model with capillary diffusion using a global pressure f...

During the late 1990s national rates of reported property and violent crime in Australia have been increasing (National Crime Statistics Unit 1997; Chilvers 1998; Cook & Leverett 1998), as have deaths from opioid overdoses. In 1996 there were 526 opioid-overdose fatalities, the majority of them involving males (Lynskey & Hall 1998). Alongside the overdose data a number of indicators from subgro...

We prove the existence of a global weak solution to the Cauchy problem for a class of 2 × 2 equations which model one-dimensional multiphase flow, and which represent a natural generalization of the scalar Buckley-Leverett equation. Loss of strict hyperbolicity (coinciding wave speeds with a (~ I) normal form) occurs on a curve in state space, and waves in a neighborhood of this curve contribut...

The objective of this paper is to report on the development of a Method of Lines (MOL) toolbox within MATLAB, and especially, on the implementation and test of a moving grid algorithm based on the equidistribution principle. This new implementation includes various spatial approximation schemes based on finite differences and slope limiters, the choice between several monitor functions, automat...

This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [J. Evol. Eq. 3 (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). The...