Approximation of scalar and vector transport problems on polyhedral meshes

Abstract : This thesis analyzes, at the continuous and at the discrete level on polyhedral meshes, the scalar and the vector transport problems in three-dimensional domains. These problems are composed of a diffusive term, an advective term, and a reactive term. In the context of Friedrichs systems, the continuous problems are analyzed in Lebesgue graph spaces. The classical positivity assumption on the Friedrichs tensor is generalized so as to consider the case of practical interest where this tensor takes null or slightly negative values. A new scheme converging at the order 3/2 is devised for the scalar advection-reaction problem using scalar degrees of freedom attached to mesh vertices. Two new schemes considering as well scalar degrees of freedom attached to mesh vertices are devised for the scalar transport problem and are robust with respect to the dominant regime. The first scheme converges at the order 1/2 when advection effects are dominant and at the order 1 when diffusion effects are dominant. The second scheme improves the accuracy by converging at the order 3/2 when advection effects are dominant. Finally, a new scheme converging at the order 1/2 is devised for the vector advection-reaction problem considering only one scalar degree of freedom per mesh edge. The accuracy and the efficiency of all these schemes are assessed on various test cases using three-dimensional polyhedral meshes
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https://pastel.archives-ouvertes.fr/tel-01419312
Contributor : Pierre Cantin <>
Submitted on : Monday, December 19, 2016 - 11:30:38 AM
Last modification on : Wednesday, January 24, 2018 - 3:14:17 AM
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Pierre Cantin. Approximation of scalar and vector transport problems on polyhedral meshes. General Mathematics [math.GM]. Université Paris-Est, 2016. English. ⟨NNT : 2016PESC1028⟩. ⟨tel-01419312⟩

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