Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, (1985) 15–28] exposed in [F. Laurent and M. Massot, (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each section...
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete finite volume space. We actually prove the convergence of the scheme in a discrete norm, with an error estimate...
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
In this paper, a class of cell centered finite volume schemes, on general unstructured meshes, for a linear convection-diffusion problem, is studied. The convection and the diffusion are respectively approximated by means of an upwind scheme and the so called diamond cell method [4]. Our main result is an error estimate of order , assuming only the (for ) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in [12]. Some...
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