This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially ...This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially adapted coordinate system.It is also designed to be equally accurate in the strongly and the mildly anisotropic cases.The method is applied to the Euler-Lorentz system,in the drift-fluid limit.This system provides a model for magnetized plasmas.展开更多
Because of stability constraints,most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar.This problem emerges with the M_(1)sy...Because of stability constraints,most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar.This problem emerges with the M_(1)system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities.Additionally,the flux term of the M_(1)system is non-linear,and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability.In this paper,we propose a numerical method that overcomes the stability constraint and preserves the realizability property.For this purpose,we relax the M_(1)system to obtain a linear flux term.Then we extend the stencil of the difference quotient to obtain stability.The scheme is applied to a radiotherapy dose calculation example.展开更多
In plasma physics domain,the electron transport is described with the FokkerPlanck-Landau equation.The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent va...In plasma physics domain,the electron transport is described with the FokkerPlanck-Landau equation.The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables.That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension.To find a solution compatible with physics conditions,the closure of the moment system is obtained under a minimum entropy principle.This model is proved to satisfy the fundamental properties like a H theorem.Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model.Finally,we validate on numerical test cases the fundamental properties of the full discrete model.展开更多
基金supported by the Marie Curie Actions of the EuropeanCommission in the frame of the DEASE project(MEST-CT-2005-021122)by the”F´ed´eration de recherche CNRS sur la fusion par confinementmagn´etique”,by theAssociation Euratom-CEA in the framework of the contract”Gyro-AP”(contract#V3629.001 avenant 1)by the University Paul Sabatier in the frame of the contract”MOSITER”.This work was performed while the first author held a post-doctoral position funded by the Fondation”Sciences et Technologies pour l’A´eronautique et l’Espace”,in the frame of the project”Plasmax”(contract#RTRA-STAE/2007/PF/002).
文摘This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially adapted coordinate system.It is also designed to be equally accurate in the strongly and the mildly anisotropic cases.The method is applied to the Euler-Lorentz system,in the drift-fluid limit.This system provides a model for magnetized plasmas.
文摘Because of stability constraints,most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar.This problem emerges with the M_(1)system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities.Additionally,the flux term of the M_(1)system is non-linear,and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability.In this paper,we propose a numerical method that overcomes the stability constraint and preserves the realizability property.For this purpose,we relax the M_(1)system to obtain a linear flux term.Then we extend the stencil of the difference quotient to obtain stability.The scheme is applied to a radiotherapy dose calculation example.
基金supported by EURATOM within the"Keep-in-Touch"activities and was granted access to the HPC resources of CINES under the allocation 2011-056129 made by GENCI(Grand Equipement National de Calcul Intensif).
文摘In plasma physics domain,the electron transport is described with the FokkerPlanck-Landau equation.The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables.That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension.To find a solution compatible with physics conditions,the closure of the moment system is obtained under a minimum entropy principle.This model is proved to satisfy the fundamental properties like a H theorem.Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model.Finally,we validate on numerical test cases the fundamental properties of the full discrete model.
