Stéphane Clain

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We present new MUSCL techniques associated with cell-centered Finite Volume method on triangular meshes. The first reconstruction consists in calculating a one vectorial slope per control volume by a minimization procedure with respect to a prescribed stability condition. The second technique we propose is based on the computation of three scalar slopes per(More)
In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic(More)
A non-negativity preserving and well-balanced scheme that exactly preserves all the smooth steady states of the shallow water system, including the moving ones, is proposed. In addition, the scheme must deal with vanishing water heights and transitions between wet and dry areas. A Godunov-type method is derived by using a relevant average of the source(More)
This paper extends the MOOD method proposed by the authors in [“A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD)”, J. Comput. Phys. 230, pp 4028-4050, (2011)], along two complementary axes: extension to very high-order polynomial reconstruction on nonconformal unstructured meshes and new Detection(More)
The Multi-dimensional Optimal Order Detection (MOOD) method for two-dimensional geometries has been introduced in “A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD)”, J. Comput. Phys. 230 (2011), and enhanced in “Improved Detection Criteria for the Multi-dimensional Optimal Order Detection (MOOD) on(More)
We consider the numerical solution of the free boundary Bernoulli problem by employing level set formulations. Using a perturbation technique, we derive a second order method that leads to a fast iteration solver. The iteration procedure is adapted in order to work in the case of topology changes. Various numerical experiments confirm the efficiency of the(More)
We present a general L stability result for a generic finite volume method for hyperbolic scalar equations coupled with a large class of reconstruction. We show that the stability is obtained if the reconstruction respects two fundamental properties: the convexity property and the sign inversion property. We also introduce a new MUSCL technique, the(More)
A mathematical model and a numerical method have been developed to simulate the mechanical and the thermal physical phenomena in a porous energy absorber during an internal arc fault in a medium voltage apparatus. A one dimensional gas flow model in porous medium with variable porosity is described. The main point is the introduction of a new numerical(More)