Perthame, B.
Overview
Works:  72 works in 150 publications in 2 languages and 1,508 library holdings 

Roles:  Author, Editor, Thesis advisor, 958, Opponent, 956 
Classifications:  QA377, 510 
Publication Timeline
.
Most widely held works by
B Perthame
Transport equations in biology by
B Perthame(
Book
)
23 editions published between 2006 and 2007 in English and held by 238 WorldCat member libraries worldwide
"This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blowup or dispersion). Original mathematical methods described are, among others, the generalized relative entropy method  a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of HamiltonJacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations."Jacket
23 editions published between 2006 and 2007 in English and held by 238 WorldCat member libraries worldwide
"This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blowup or dispersion). Original mathematical methods described are, among others, the generalized relative entropy method  a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of HamiltonJacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations."Jacket
Kinetic formulation of conservation laws by
B Perthame(
Book
)
10 editions published between 2002 and 2010 in English and held by 198 WorldCat member libraries worldwide
&Quot;Kinetic Formulation of Conservation Laws gives a general presentation of the mathematical connections between kinetic theory and conservation laws. The kinetic formalism approach allows the reader to consider partial differential equations, such as some nonlinear conservation laws, as linear kinetic (or semikinetic) equations acting on a nonlinear quantity. It also provides the reader with Fourier transform, regularization, and moments methods as new approaches for the investigation of uniqueness, regularizing effects, and a priori bounds."BOOK JACKET
10 editions published between 2002 and 2010 in English and held by 198 WorldCat member libraries worldwide
&Quot;Kinetic Formulation of Conservation Laws gives a general presentation of the mathematical connections between kinetic theory and conservation laws. The kinetic formalism approach allows the reader to consider partial differential equations, such as some nonlinear conservation laws, as linear kinetic (or semikinetic) equations acting on a nonlinear quantity. It also provides the reader with Fourier transform, regularization, and moments methods as new approaches for the investigation of uniqueness, regularizing effects, and a priori bounds."BOOK JACKET
On positively preserving finite volume schemes for compressible Euler Equations by
B Perthame(
Book
)
1 edition published in 1993 in English and held by 79 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 79 WorldCat member libraries worldwide
Modeling of collisions by
A Decoster(
Book
)
7 editions published between 1997 and 1998 in English and French and held by 76 WorldCat member libraries worldwide
7 editions published between 1997 and 1998 in English and French and held by 76 WorldCat member libraries worldwide
A kinetic equation with kinetic entropy functions for scalar conservation laws by
B Perthame(
Book
)
4 editions published in 1990 in English and held by 74 WorldCat member libraries worldwide
We construct a nonlinear kinetic equation and prove that it is well adapted to describe general multidimensional scalar conservation laws. In particular we prove that it is wellposed uniformly in epsilon  the microscopic scale. We also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions  analogous to Boltzmann's microscopic Hfunction, such that they recover Krushkovtype entropy inequality on the macroscopic scale. Finally, we prove by both  BV compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case, that the local density of kinetic particles admits a 'continuum' limit, as it converges strongly with epsilon down to 0 to the unique entropy solution of the corresponding conversation law. (Author) (kr)
4 editions published in 1990 in English and held by 74 WorldCat member libraries worldwide
We construct a nonlinear kinetic equation and prove that it is well adapted to describe general multidimensional scalar conservation laws. In particular we prove that it is wellposed uniformly in epsilon  the microscopic scale. We also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions  analogous to Boltzmann's microscopic Hfunction, such that they recover Krushkovtype entropy inequality on the macroscopic scale. Finally, we prove by both  BV compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case, that the local density of kinetic particles admits a 'continuum' limit, as it converges strongly with epsilon down to 0 to the unique entropy solution of the corresponding conversation law. (Author) (kr)
Kinetic equations and asymptotic theory by
François Bouchut(
Book
)
4 editions published in 2000 in English and held by 72 WorldCat member libraries worldwide
4 editions published in 2000 in English and held by 72 WorldCat member libraries worldwide
Advances in kinetic theory and computing : selected papers(
Book
)
9 editions published in 1994 in English and held by 71 WorldCat member libraries worldwide
This selection of eight papers discusses "Equations of Kinetic Physics" with emphasis on analysis, modelling and computing. The first three papers are on numerical methods for VlasovPoisson and VlasovMaxwell Equations  comparison between particles and Eulerian methods (G. Manfredi and M.R. Feix), computing BGK instability with Eulerian codes (M.R Feix, Pertrand & A. Ghieco) and coupling particles and Eulerian methods (S. MasGallic and P.A. Raviart)  followed by a survey of kinetic and macroscopic models for semiconductor devices  Boltzmann equation, driftdiffusion models (F. Poupaud). In addition, there are two papers on the modelling and analysis of singular perturbation problems arising in plasma physics  derivation of the ChildLagmuyr emission laws (P. Degond) and Euler models with small pressure terms (F. Bouchut)  followed by two papers on the analysis and numerical analysis of the Boltzmann equations  symmetry properties in the polynomials arising in ChapmanEnskog expansion (L. Desvillettes and F. Golse) and a general introduction to computing the Boltzmann equations with random particle methods (B. Perthame)
9 editions published in 1994 in English and held by 71 WorldCat member libraries worldwide
This selection of eight papers discusses "Equations of Kinetic Physics" with emphasis on analysis, modelling and computing. The first three papers are on numerical methods for VlasovPoisson and VlasovMaxwell Equations  comparison between particles and Eulerian methods (G. Manfredi and M.R. Feix), computing BGK instability with Eulerian codes (M.R Feix, Pertrand & A. Ghieco) and coupling particles and Eulerian methods (S. MasGallic and P.A. Raviart)  followed by a survey of kinetic and macroscopic models for semiconductor devices  Boltzmann equation, driftdiffusion models (F. Poupaud). In addition, there are two papers on the modelling and analysis of singular perturbation problems arising in plasma physics  derivation of the ChildLagmuyr emission laws (P. Degond) and Euler models with small pressure terms (F. Bouchut)  followed by two papers on the analysis and numerical analysis of the Boltzmann equations  symmetry properties in the polynomials arising in ChapmanEnskog expansion (L. Desvillettes and F. Golse) and a general introduction to computing the Boltzmann equations with random particle methods (B. Perthame)
Parabolic equations in biology : growth, reaction, movement and diffusion by
B Perthame(
Book
)
8 editions published in 2015 in English and held by 28 WorldCat member libraries worldwide
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reactiondiffusion systems, invasion waves and FokkerPlanck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blowup in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for masterlevel coursework
8 editions published in 2015 in English and held by 28 WorldCat member libraries worldwide
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reactiondiffusion systems, invasion waves and FokkerPlanck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blowup in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for masterlevel coursework
Dispersion and moment lemmas revisited by
Ingenuin Gasser(
)
3 editions published between 1998 and 2000 in English and held by 13 WorldCat member libraries worldwide
3 editions published between 1998 and 2000 in English and held by 13 WorldCat member libraries worldwide
SUR QUELQUES PROBLEMES DE CONTROLE OPTIMAL ET DE THEORIES CINETIQUES ET LEUR APPROXIMATION NUMERIQUE by
B Perthame(
Book
)
3 editions published in 1987 in French and English and held by 6 WorldCat member libraries worldwide
CETTE THESE EST DIVISEE EN TROIS PARTIES OU L'ON ETUDIE DES EQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES. A. EQUATIONS DE HAMILTONJACOBI ET CONTROLE OPTIMAL. DANS UN PREMIER CHAPITRE, ON S'INTERESSE AUX INEQUATIONS QUASIVARIATIONNELLES ASSOCIEES AUX EQUATIONS DE HAMILTONJACOBIEELLMANN. ON DONNE UNE CONDITION ASSURANT L'EXISTENCE D'UNE SOLUTION CONTINUE. CECI PERMET D'ETUDIER DIVERS PROBLEMES RELIES AU CONTROLE IMPULSIONNEL DE DIFFUSIONS : CONTRAINTES D'ETAT, REGULARITE FORTE, CONTROLE ERGODIQUE. DANS UN DEUXIEME CHAPITRE, ON DONNE DIFFERENTES EXTENSIONS DE LA NOTION DE SOLUTION DE VISCOSITE D'EQUATIONS DE HAMILTONJACOBI DU PREMIER ORDRE AFIN DE TRAITER LES CAS DE CONDITIONS DE NEUMANN, D'HAMILTONIENS DISCONTINUS EN TEMPS OU D'OBSTACLES DISCONTINUS. B. EQUATION DE TRANSPORT ET PROBLEMES ASYMPTOTIQUES. DANS CETTE PARTIE, ON ETUDIE PRINCIPALEMENT LES EQUATIONS DU TRANSFERT RADIATIF ET LEUR APPROXIMATION PAR UNE EQUATION ELLIPTIQUE NONLINEAIRE DEGENEREE DU TYPE MILIEUX POREUX. ON UTILISE POUR CELA DEUX TYPES DE TECHNIQUES : LA THEORIE DES SEMIGROUPES ACCRETIFS DANS UN ESPACE DE BANACH GENERAL OU BIEN DES METHODES DE COMPACITE. C. ADAPTATION IMPLICITE DE MAILLAGE EN DYNAMIQUE DES GAZ MONODIMENSIONNELLE. NOUS ABORDONS LE PROBLEME DU CALCUL NUMERIQUE DE DISCONTINUITES (CHOC) PAR DES METHODES DE MAILLAGE ADAPTATIF. LES EQUATIONS SONT DISCRETISEES DE MANIERE IMPLICITE ET COUPLEES A UNE EQUATION (IMPLICITE) DETERMINANT LE NOUVEAU MAILLAGE
3 editions published in 1987 in French and English and held by 6 WorldCat member libraries worldwide
CETTE THESE EST DIVISEE EN TROIS PARTIES OU L'ON ETUDIE DES EQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES. A. EQUATIONS DE HAMILTONJACOBI ET CONTROLE OPTIMAL. DANS UN PREMIER CHAPITRE, ON S'INTERESSE AUX INEQUATIONS QUASIVARIATIONNELLES ASSOCIEES AUX EQUATIONS DE HAMILTONJACOBIEELLMANN. ON DONNE UNE CONDITION ASSURANT L'EXISTENCE D'UNE SOLUTION CONTINUE. CECI PERMET D'ETUDIER DIVERS PROBLEMES RELIES AU CONTROLE IMPULSIONNEL DE DIFFUSIONS : CONTRAINTES D'ETAT, REGULARITE FORTE, CONTROLE ERGODIQUE. DANS UN DEUXIEME CHAPITRE, ON DONNE DIFFERENTES EXTENSIONS DE LA NOTION DE SOLUTION DE VISCOSITE D'EQUATIONS DE HAMILTONJACOBI DU PREMIER ORDRE AFIN DE TRAITER LES CAS DE CONDITIONS DE NEUMANN, D'HAMILTONIENS DISCONTINUS EN TEMPS OU D'OBSTACLES DISCONTINUS. B. EQUATION DE TRANSPORT ET PROBLEMES ASYMPTOTIQUES. DANS CETTE PARTIE, ON ETUDIE PRINCIPALEMENT LES EQUATIONS DU TRANSFERT RADIATIF ET LEUR APPROXIMATION PAR UNE EQUATION ELLIPTIQUE NONLINEAIRE DEGENEREE DU TYPE MILIEUX POREUX. ON UTILISE POUR CELA DEUX TYPES DE TECHNIQUES : LA THEORIE DES SEMIGROUPES ACCRETIFS DANS UN ESPACE DE BANACH GENERAL OU BIEN DES METHODES DE COMPACITE. C. ADAPTATION IMPLICITE DE MAILLAGE EN DYNAMIQUE DES GAZ MONODIMENSIONNELLE. NOUS ABORDONS LE PROBLEME DU CALCUL NUMERIQUE DE DISCONTINUITES (CHOC) PAR DES METHODES DE MAILLAGE ADAPTATIF. LES EQUATIONS SONT DISCRETISEES DE MANIERE IMPLICITE ET COUPLEES A UNE EQUATION (IMPLICITE) DETERMINANT LE NOUVEAU MAILLAGE
MODELES DE TRANSPORT D'ENERGIE DES SEMICONDUCTEURS, ETUDES ASYMPTOTIQUES ET RESOLUTION PAR DES ELEMENTS FINIS MIXTES by PHILIPPE MONTARNAL(
Book
)
1 edition published in 1997 in French and held by 4 WorldCat member libraries worldwide
NOUS NOUS INTERESSONS DANS CE TRAVAIL A L'ETUDE MATHEMATIQUE ET A LA SIMULATION DES MODELES DE SEMICONDUCTEURS INCLUANT UNE EQUATION D'ENERGIE. CE TRAVAIL SE DECOMPOSE EN TROIS PARTIES PRINCIPALES. LA PREMIERE PARTIE EST CONSACREE A L'ANALYSE ASYMPTOTIQUE DE L'EQUATION DE DERIVEDIFFUSION DANS LE CAS OU LE TERME DE DIFFUSION DEVIENT NEGLIGEABLE. NOUS MONTRONS QUE LE PROBLEME LIMITE S'EXPRIME SOUS LA FORME D'UN SYSTEME COUPLE EQUATION DE HAMILTONJACOBI  INEQUATIONS VARIATIONNELLES. DANS LE CAS UNIDIMENSIONNEL NOUS PROUVONS L'UNICITE DE CE PROBLEME LIMITE. DANS LA SECONDE PARTIE, NOUS DERIVONS UN MODELE HYDRODYNAMIQUE DES SEMICONDUCTEURS A PARTIR D'UNE EQUATION DE TRANSPORT DE BOLTZMANN CONTENANT DIFFERENTES ECHELLES DE COLLISION. CETTE FORMULATION GENERALISE LES DEUX APPROCHES ACTUELLES (HYDRODYNAMIQUE CLASSIQUE ET TRANSPORT D'ENERGIE). DE PLUS, LE MODELE PROPOSE ADMET UNE FONCTION D'ENTROPIE GLOBALE ET UNE FORME SYMETRIQUE. ENFIN, LA TROISIEME PARTIE CONCERNE LA SIMULATION BIDIMENSIONNELLE DE MODELES HYDRODYNAMIQUE SIMPLIFIE ET DE TRANSPORT D'ENERGIE POUR DES SEMICONDUCTEURS A HETEROJONCTIONS. LES METHODES NUMERIQUES UTILISEES COMBINENT DES TECHNIQUES DE TRANSITOIRE ARTIFICIEL, DE RELAXATION PAR BLOCS, DES SCHEMAS DE TYPE ELEMENTS FINIS MIXTES, DES ALGORITHMES DE NEWTONRAPHSON ET DE GMRES. NOUS PRESENTONS DIFFERENTS RESULTATS DE SIMULATION SUR DES DISPOSITIFS REELS (TRANSISTORS JFET ET HEMT)
1 edition published in 1997 in French and held by 4 WorldCat member libraries worldwide
NOUS NOUS INTERESSONS DANS CE TRAVAIL A L'ETUDE MATHEMATIQUE ET A LA SIMULATION DES MODELES DE SEMICONDUCTEURS INCLUANT UNE EQUATION D'ENERGIE. CE TRAVAIL SE DECOMPOSE EN TROIS PARTIES PRINCIPALES. LA PREMIERE PARTIE EST CONSACREE A L'ANALYSE ASYMPTOTIQUE DE L'EQUATION DE DERIVEDIFFUSION DANS LE CAS OU LE TERME DE DIFFUSION DEVIENT NEGLIGEABLE. NOUS MONTRONS QUE LE PROBLEME LIMITE S'EXPRIME SOUS LA FORME D'UN SYSTEME COUPLE EQUATION DE HAMILTONJACOBI  INEQUATIONS VARIATIONNELLES. DANS LE CAS UNIDIMENSIONNEL NOUS PROUVONS L'UNICITE DE CE PROBLEME LIMITE. DANS LA SECONDE PARTIE, NOUS DERIVONS UN MODELE HYDRODYNAMIQUE DES SEMICONDUCTEURS A PARTIR D'UNE EQUATION DE TRANSPORT DE BOLTZMANN CONTENANT DIFFERENTES ECHELLES DE COLLISION. CETTE FORMULATION GENERALISE LES DEUX APPROCHES ACTUELLES (HYDRODYNAMIQUE CLASSIQUE ET TRANSPORT D'ENERGIE). DE PLUS, LE MODELE PROPOSE ADMET UNE FONCTION D'ENTROPIE GLOBALE ET UNE FORME SYMETRIQUE. ENFIN, LA TROISIEME PARTIE CONCERNE LA SIMULATION BIDIMENSIONNELLE DE MODELES HYDRODYNAMIQUE SIMPLIFIE ET DE TRANSPORT D'ENERGIE POUR DES SEMICONDUCTEURS A HETEROJONCTIONS. LES METHODES NUMERIQUES UTILISEES COMBINENT DES TECHNIQUES DE TRANSITOIRE ARTIFICIEL, DE RELAXATION PAR BLOCS, DES SCHEMAS DE TYPE ELEMENTS FINIS MIXTES, DES ALGORITHMES DE NEWTONRAPHSON ET DE GMRES. NOUS PRESENTONS DIFFERENTS RESULTATS DE SIMULATION SUR DES DISPOSITIFS REELS (TRANSISTORS JFET ET HEMT)
Leçons de mathématiques d'aujourd'hui by
JeanPierre Kahane(
Book
)
3 editions published in 2007 in French and held by 4 WorldCat member libraries worldwide
3 editions published in 2007 in French and held by 4 WorldCat member libraries worldwide
MODELISATION ET CALCUL PARALLELE D'UNE COUCHE LIMITE CINETIQUE by JEANPHILIPPE PERLAT(
Book
)
1 edition published in 1998 in French and held by 4 WorldCat member libraries worldwide
A HAUTES ALTITUDES OU EN REGIMES RAREFIES, UN GAZ EST MODELISE A L'ECHELLE MICROSCOPIQUE, COMME UNE MULTITUDE DE PARTICULES CARACTERISEES PAR LEUR VITESSE ET LEUR POSITION. L'EQUATION MATHEMATIQUE DU MODELE EST L'EQUATION DE BOLTZMANN, QUI DECRIT L'EVOLUTION D'UNE FONCTION DE DISTRIBUTION DE VITESSE ET DE POSITION DE CES PARTICULES ET QUI PEUT ETRE NUMERIQUEMENT RESOLUE PAR DES METHODES DE MONTE CARLO. LE REGIME TRANSITIONNEL CARACTERISE PAR UN NOMBRE DE KNUDSEN (LE RAPPORT ENTRE LE LIBRE PARCOURS MOYEN ET UNE ECHELLE CARACTERISTIQUE DE L'ECOULEMENT) ENTRE 0.001 ET 0.1, EST PLUS DIFFICILE A MODELISER. AFIN DE REPONDRE AUX DOUBLES PROBLEMES DE TEMPS DE CALCUL ET DE PLACE MEMOIRE DES METHODES DE MONTE CARLO POUR CE REGIME, NOUS DEVELOPPONS PREMIEREMENT UN CODE PARALLELE AVEC DECOMPOSITION DE DOMAINE. UNE AUTRE STRATEGIE UTILISE DES EQUATIONS AUX MOMENTS, OBTENUES PAR L'INTEGRATION PONDEREE DE L'EQUATION DE BOLTZMANN SUR L'ESPACE DES VITESSES, ET FERMEES EN SUPPOSANT QUE LA FONCTION DE DISTRIBUTION EST DE LA FORME F(X)=EXP((X,T).M(V)). LE MODELE DE LEVERMORE AINSI APPELE EST DECRIT MATHEMATIQUEMENT ET NUMERIQUEMENT. EN PARTICULIER, NOUS PROPOSONS DES CONDITIONS AUX LIMITES CONSISTANTES AU MODELE ASYMPTOTIQUE ET DEVELOPPONS UN SCHEMA NUMERIQUE DU PREMIER ORDRE D'ORIGINE CINETIQUE POUR LE SYSTEME AUX MOMENTS DE LEVERMORE RESULTANT. ENFIN, NOUS PRESENTONS UNE STRATEGIE GENERALE POUR LA RESOLUTION DE PROBLEMES D'ECOULEMENTS EN REGIME TRANSITIONNEL, COUPLANT LES EQUATIONS DE LEVERMORE UTILISEES DANS LA REGION RAREFIEE, AUX EQUATIONS DE NAVIERSTOKES RESOLUES DANS LA REGION FLUIDE. DES RESULTATS NUMERIQUES SONT PRESENTES POUR VALIDER CETTE STRATEGIE DE COUPLAGE
1 edition published in 1998 in French and held by 4 WorldCat member libraries worldwide
A HAUTES ALTITUDES OU EN REGIMES RAREFIES, UN GAZ EST MODELISE A L'ECHELLE MICROSCOPIQUE, COMME UNE MULTITUDE DE PARTICULES CARACTERISEES PAR LEUR VITESSE ET LEUR POSITION. L'EQUATION MATHEMATIQUE DU MODELE EST L'EQUATION DE BOLTZMANN, QUI DECRIT L'EVOLUTION D'UNE FONCTION DE DISTRIBUTION DE VITESSE ET DE POSITION DE CES PARTICULES ET QUI PEUT ETRE NUMERIQUEMENT RESOLUE PAR DES METHODES DE MONTE CARLO. LE REGIME TRANSITIONNEL CARACTERISE PAR UN NOMBRE DE KNUDSEN (LE RAPPORT ENTRE LE LIBRE PARCOURS MOYEN ET UNE ECHELLE CARACTERISTIQUE DE L'ECOULEMENT) ENTRE 0.001 ET 0.1, EST PLUS DIFFICILE A MODELISER. AFIN DE REPONDRE AUX DOUBLES PROBLEMES DE TEMPS DE CALCUL ET DE PLACE MEMOIRE DES METHODES DE MONTE CARLO POUR CE REGIME, NOUS DEVELOPPONS PREMIEREMENT UN CODE PARALLELE AVEC DECOMPOSITION DE DOMAINE. UNE AUTRE STRATEGIE UTILISE DES EQUATIONS AUX MOMENTS, OBTENUES PAR L'INTEGRATION PONDEREE DE L'EQUATION DE BOLTZMANN SUR L'ESPACE DES VITESSES, ET FERMEES EN SUPPOSANT QUE LA FONCTION DE DISTRIBUTION EST DE LA FORME F(X)=EXP((X,T).M(V)). LE MODELE DE LEVERMORE AINSI APPELE EST DECRIT MATHEMATIQUEMENT ET NUMERIQUEMENT. EN PARTICULIER, NOUS PROPOSONS DES CONDITIONS AUX LIMITES CONSISTANTES AU MODELE ASYMPTOTIQUE ET DEVELOPPONS UN SCHEMA NUMERIQUE DU PREMIER ORDRE D'ORIGINE CINETIQUE POUR LE SYSTEME AUX MOMENTS DE LEVERMORE RESULTANT. ENFIN, NOUS PRESENTONS UNE STRATEGIE GENERALE POUR LA RESOLUTION DE PROBLEMES D'ECOULEMENTS EN REGIME TRANSITIONNEL, COUPLANT LES EQUATIONS DE LEVERMORE UTILISEES DANS LA REGION RAREFIEE, AUX EQUATIONS DE NAVIERSTOKES RESOLUES DANS LA REGION FLUIDE. DES RESULTATS NUMERIQUES SONT PRESENTES POUR VALIDER CETTE STRATEGIE DE COUPLAGE
A new variant of Van Leer's method for multidimensional systems of conservation laws by
B Perthame(
Book
)
3 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We give a new interpretation of Van Leer's construction of second order accurate upwind schemes for hyperbolic systems of conservation laws. It consists in first interpolating values at the nodes of the mesh, then correcting them globally on each cell by a conservation argument. This leads to represent functions, no longer as piecewise linear, but as piecewise constant in subcells. It can be used on a rectangular, triangular or mediane based dual grid to get a genuinely multidimensional scheme, and also to prove that the second order scheme gives non negative values of the pressure and density for gas dynamics, even on an unstructured mesh. Thus this approach is very robust."
3 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We give a new interpretation of Van Leer's construction of second order accurate upwind schemes for hyperbolic systems of conservation laws. It consists in first interpolating values at the nodes of the mesh, then correcting them globally on each cell by a conservation argument. This leads to represent functions, no longer as piecewise linear, but as piecewise constant in subcells. It can be used on a rectangular, triangular or mediane based dual grid to get a genuinely multidimensional scheme, and also to prove that the second order scheme gives non negative values of the pressure and density for gas dynamics, even on an unstructured mesh. Thus this approach is very robust."
Maximum principle on the entropy and minimal limitations for kinetic schemes = Principe du maximum sur l'entropie et limiteurs
pour schemas cinetiques by
Brahim Khobalatte(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We consider kinetic schemes for the multidimensional inviscid gaz dynamics equations (compressible Euler equations). We prove that the discrete maximum principle holds for a special convex entropy. This fixes the choice of the equilibrium functions necessary for kinetic schemes. We use this property to perform a second order oscilation free scheme where only one slope limitation (for three conserved quantities in 1d) is necessary. Numerical results assert the strong convergence of the scheme."
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We consider kinetic schemes for the multidimensional inviscid gaz dynamics equations (compressible Euler equations). We prove that the discrete maximum principle holds for a special convex entropy. This fixes the choice of the equilibrium functions necessary for kinetic schemes. We use this property to perform a second order oscilation free scheme where only one slope limitation (for three conserved quantities in 1d) is necessary. Numerical results assert the strong convergence of the scheme."
Vers une modélisation mathématique de la filtration des globules blancs du sang by
Mohamed Belhadj(
Book
)
1 edition published in 2005 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 2005 in French and held by 3 WorldCat member libraries worldwide
ANALYSE NUMERIQUE DES EQUATIONS CINETIQUES ET DE LEURS LIMITES HYDRODYNAMIQUES by
Stéphane Mischler(
Book
)
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
CETTE THESE ABORDE L'ETUDE THEORIQUE ET NUMERIQUE DES EQUATIONS CINETIQUES COLLISIONNELLES (EQ. DE BOLTZMANN ET EQ. BGK) ET DE LEUR LIMITE FLUIDE (SYSTEME D'EQUATIONS D'EULER EN COMPRESSIBLE). DANS LA PREMIERE PARTIE NOUS MONTRONS L'UNICITE DE LA SOLUTION DU PROBLEME DE CAUCHY DE L'EQUATION BGK AVEC DONNEE INITIALE BORNEE SUPERIEUREMENT ET INFERIEUREMENT POUR UNE NORME UNIFORME AVEC POIDS POLYNOMIAL EN VITESSE ET EN POSITION. LORSQUE LA DONNEE INITIALE EST, DE PLUS, A VARIATIONS BORNEES, NOUS RESOLVONS UN SCHEMA SEMIDISCRET EN TEMPS ET NOUS MONTRONS QU'IL CONVERGE AVEC UN TAUX D'ORDRE UN DEMI. LA SECONDE PARTIE CONCERNE LES SOLUTIONS RENORMALISEES DE L'EQUATION DE BOLTZMANN. NOUS PROUVONS LA CONVERGENCE DE LA METHODE DE DECOMPOSITION D'OPERATEUR ENTRE PARTIE TRANSPORT ET PARTIE COLLISION POUR LES EQUATIONS DE BOLTZMANN ET BGK. LA DIFFICULTE PRINCIPALE EST DE MONTRER LA COMPACITE FORTE DES MOYENNES EN VITESSES DE LA SUITE DES SOLUTIONS APPROCHEES DEFINIES PAR LA DECOMPOSITION. NOUS NOUS INTERESSONS A LA DISCRETISATION EN VITESSE DE L'EQUATION DE BOLTZMANN PAR DES SYSTEMES D'EQUATIONS DE BOLTZMANN DISCRETES. NOUS DONNONS UN CRITERE GENERAL DE CONVERGENCE QUE NOUS APPLIQUONS POUR DEMONTRER LA CONVERGENCE DE DIFFERENTS SCHEMAS. DEUX DIFFICULTES APPARAISSENT : NOUS DEVONS TRAITER DES SECTIONS EFFICACES NON STANDARD, ET DEMONTRER UN THEOREME DE COMPACITE FORTE DES MOYENNES EN VITESSE ADAPTE A CE CONTEXTE. NOUS DEMONTRONS DES THEOREMES D'EXISTENCE DE SOLUTIONS DE L'EQUATION DE BOLTZMANN POUR DES DONNEES INITIALES D'ENERGIE INFINIE, CE QUI GENERALISE LARGEMENT LES DONNEES INITIALES POSSIBLES. CETTE METHODE PEUT S'APPLIQUER A LA THEORIE DES SOLUTIONS RENORMALISEES (GRANDES ET GLOBALES) ET A CELLE DES SOLUTIONS DISTRIBUTIONS (PETITES ET GLOBALES, OU PROCHES D'UNE MAXWELLIENNE ET GLOBALES). LA TROISIEME PARTIE EST CONSACREE A UNE ETUDE NUMERIQUE DE SCHEMAS DE TYPE CINETIQUE COLLISIONNEL POUR LES EQUATIONS D'EULER. NOUS CONSTRUISONS UN SCHEMA PRECIS SUR LES DISCONTINUITES DE CONTACT GRACE A UNE FORMULATION CINETIQUE EXACTE DE L'EQUATION D'EULER ET UNE DISCRETISATION DE CETTE EQUATION
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
CETTE THESE ABORDE L'ETUDE THEORIQUE ET NUMERIQUE DES EQUATIONS CINETIQUES COLLISIONNELLES (EQ. DE BOLTZMANN ET EQ. BGK) ET DE LEUR LIMITE FLUIDE (SYSTEME D'EQUATIONS D'EULER EN COMPRESSIBLE). DANS LA PREMIERE PARTIE NOUS MONTRONS L'UNICITE DE LA SOLUTION DU PROBLEME DE CAUCHY DE L'EQUATION BGK AVEC DONNEE INITIALE BORNEE SUPERIEUREMENT ET INFERIEUREMENT POUR UNE NORME UNIFORME AVEC POIDS POLYNOMIAL EN VITESSE ET EN POSITION. LORSQUE LA DONNEE INITIALE EST, DE PLUS, A VARIATIONS BORNEES, NOUS RESOLVONS UN SCHEMA SEMIDISCRET EN TEMPS ET NOUS MONTRONS QU'IL CONVERGE AVEC UN TAUX D'ORDRE UN DEMI. LA SECONDE PARTIE CONCERNE LES SOLUTIONS RENORMALISEES DE L'EQUATION DE BOLTZMANN. NOUS PROUVONS LA CONVERGENCE DE LA METHODE DE DECOMPOSITION D'OPERATEUR ENTRE PARTIE TRANSPORT ET PARTIE COLLISION POUR LES EQUATIONS DE BOLTZMANN ET BGK. LA DIFFICULTE PRINCIPALE EST DE MONTRER LA COMPACITE FORTE DES MOYENNES EN VITESSES DE LA SUITE DES SOLUTIONS APPROCHEES DEFINIES PAR LA DECOMPOSITION. NOUS NOUS INTERESSONS A LA DISCRETISATION EN VITESSE DE L'EQUATION DE BOLTZMANN PAR DES SYSTEMES D'EQUATIONS DE BOLTZMANN DISCRETES. NOUS DONNONS UN CRITERE GENERAL DE CONVERGENCE QUE NOUS APPLIQUONS POUR DEMONTRER LA CONVERGENCE DE DIFFERENTS SCHEMAS. DEUX DIFFICULTES APPARAISSENT : NOUS DEVONS TRAITER DES SECTIONS EFFICACES NON STANDARD, ET DEMONTRER UN THEOREME DE COMPACITE FORTE DES MOYENNES EN VITESSE ADAPTE A CE CONTEXTE. NOUS DEMONTRONS DES THEOREMES D'EXISTENCE DE SOLUTIONS DE L'EQUATION DE BOLTZMANN POUR DES DONNEES INITIALES D'ENERGIE INFINIE, CE QUI GENERALISE LARGEMENT LES DONNEES INITIALES POSSIBLES. CETTE METHODE PEUT S'APPLIQUER A LA THEORIE DES SOLUTIONS RENORMALISEES (GRANDES ET GLOBALES) ET A CELLE DES SOLUTIONS DISTRIBUTIONS (PETITES ET GLOBALES, OU PROCHES D'UNE MAXWELLIENNE ET GLOBALES). LA TROISIEME PARTIE EST CONSACREE A UNE ETUDE NUMERIQUE DE SCHEMAS DE TYPE CINETIQUE COLLISIONNEL POUR LES EQUATIONS D'EULER. NOUS CONSTRUISONS UN SCHEMA PRECIS SUR LES DISCONTINUITES DE CONTACT GRACE A UNE FORMULATION CINETIQUE EXACTE DE L'EQUATION D'EULER ET UNE DISCRETISATION DE CETTE EQUATION
Méthodes de relaxation pour la simulation des écoulements polyphasiques dans les conduites pétrolières by
Michaël Baudin(
Book
)
2 editions published between 2003 and 2007 in French and held by 3 WorldCat member libraries worldwide
2 editions published between 2003 and 2007 in French and held by 3 WorldCat member libraries worldwide
Contribution à la simulation numérique des écoulements de gas raréfiés by Yacin Bahi(
Book
)
1 edition published in 1997 in French and held by 3 WorldCat member libraries worldwide
LA SIMULATION D'ECOULEMENTS DE GAZ RAREFIES FAIT INTERVENIR L'ETUDE DE MODELES CINETIQUES, GOUVERNES PAR L'EQUATION DE BOLTZMANN. CETTE ETUDE ABORDE DEUX ASPECTS FONDAMENTAUX DE LA RESOLUTION DE CETTE EQUATION PAR DES METHODES DETERMINISTES. LA PREMIERE PARTIE DE CETTE THESE PROCEDE A LA REDUCTION DU COUT DE CES METHODES DANS LE CADRE DE MODELES DE GAZ MONOATOMIQUES. AINSI UN SCHEMA DE COUPLAGE DIRECT D'UN MODELE DETERMINISTE AVEC DIFFERENTS SCHEMAS DE LA MECANIQUE DES FLUIDES EST PROPOSE PAR LE BIAIS D'UNE MISE EN UVRE SUR CALCULATEUR PARALLELE. LA DEUXIEME PARTIE PROPOSE UN SCHEMA DETERMINISTE POUR DES MODELES DE GAZ POLYATOMIQUES, INSPIRE D'APPROCHES EXISTANTES DANS LE CADRE MONOATOMIQUE. UNE ANALYSE ALGORITHMIQUE POUSSEE AINSI QU'UNE MISE EN UVRE SUR CALCULATEUR PARALLELE PERMET D'ABORDER DES PROBLEMES REALISTES
1 edition published in 1997 in French and held by 3 WorldCat member libraries worldwide
LA SIMULATION D'ECOULEMENTS DE GAZ RAREFIES FAIT INTERVENIR L'ETUDE DE MODELES CINETIQUES, GOUVERNES PAR L'EQUATION DE BOLTZMANN. CETTE ETUDE ABORDE DEUX ASPECTS FONDAMENTAUX DE LA RESOLUTION DE CETTE EQUATION PAR DES METHODES DETERMINISTES. LA PREMIERE PARTIE DE CETTE THESE PROCEDE A LA REDUCTION DU COUT DE CES METHODES DANS LE CADRE DE MODELES DE GAZ MONOATOMIQUES. AINSI UN SCHEMA DE COUPLAGE DIRECT D'UN MODELE DETERMINISTE AVEC DIFFERENTS SCHEMAS DE LA MECANIQUE DES FLUIDES EST PROPOSE PAR LE BIAIS D'UNE MISE EN UVRE SUR CALCULATEUR PARALLELE. LA DEUXIEME PARTIE PROPOSE UN SCHEMA DETERMINISTE POUR DES MODELES DE GAZ POLYATOMIQUES, INSPIRE D'APPROCHES EXISTANTES DANS LE CADRE MONOATOMIQUE. UNE ANALYSE ALGORITHMIQUE POUSSEE AINSI QU'UNE MISE EN UVRE SUR CALCULATEUR PARALLELE PERMET D'ABORDER DES PROBLEMES REALISTES
On positivity preserving finite volume schemes for compressible Euler equations by
Institute for Computer Applications in Science and Engineering(
Book
)
3 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide
We consider positivity preserving property of first and higher order finite volume schemes for one and two dimensional compressible Euler equations of gas dynamics. A general framework is established which shows the positivity of density and pressure whenever the underlying one dimensional first order building block based on exact or approximate Riemann solver and the reconstruction are both positivity preserving. Appropriate limitation to achieve high order positivity preserving reconstruction is described. Finite volume schemes, Gas dynamics, Stability, Positivity preserving
3 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide
We consider positivity preserving property of first and higher order finite volume schemes for one and two dimensional compressible Euler equations of gas dynamics. A general framework is established which shows the positivity of density and pressure whenever the underlying one dimensional first order building block based on exact or approximate Riemann solver and the reconstruction are both positivity preserving. Appropriate limitation to achieve high order positivity preserving reconstruction is described. Finite volume schemes, Gas dynamics, Stability, Positivity preserving
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Useful Links
Associated Subjects
Biomathematics Collisions (Nuclear physics) Collisions (Physics)Mathematical models Computational biology Conservation laws (Mathematics) Differentiable dynamical systems Differential equations Differential equations, Parabolic Differential equations, Partial Differential equations, PartialAsymptotic theory Differential equationsAsymptotic theory Engineering mathematics Finite element method Gas dynamics Kinetic theory of gases Kinetic theory of matter Lagrange equations Mathematical physics Mathematics Natural history Number theory Population biologyMathematical models Quantum field theory Science