In this work we construct high-resolution numerical schemes for the calculation of quasi-1D unsteady flow in pipes with variable cross-sectional area. This is an example non-homogeneous hyperbolic systems conservation laws that admit stationary solutions. We use strategy developed by authors [1] which to transform system into homogeneous writing source term divergence form, so it can be incorpo...

Aims. This work presents a new hydrodynamical algorithm to study astrophysical detonations. A prime motivation of this development is the description of a carbon detonation in conditions relevant to superbursts, which are thought to result from the propagation of a detonation front around the surface of a neutron star in the carbon layer underlying the atmosphere. Methods. The algorithm we have...

The aim of this work is to derive a well-balanced numerical scheme to approximate the solutions of the Euler equations with a gravitational potential. This system admits an infinity of steady state solutions which are not all known in an explicit way. Among all these solutions, the hydrostatic atmosphere has a special physical interest. We develop an approximate Riemann solver using the formali...

This paper concerns the numerical schemes describing solute transport in fissured systems which are characterized by the tectonic blocks and spatial repartition of hydraulic properties with dual permeability structures composed of highand low-permeability blocks of the chalk aquifer (Northern France). Both advection and diffusion mechanisms are taken into account. The novel mathematical approac...

An efficient implementation technique of a block matrix implicit operator based on van Leer’s FVS scheme is proposed for the LU-SGS method on unstructured meshes. The off-diagonal terms of the linear system of equations were approximated by the increment of the numerical flux using the point-by-point splitting feature of FVS schemes. The present improved LU-SGS method provides better performanc...