Search results for "hydrodynamic limit"

showing 4 items of 4 documents

A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures

2016

In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.

Binary numberKinetic energy01 natural sciencesBoltzmann equationPhysics::Fluid Dynamics35Q20 35B25 82C40 76T15 76D07symbols.namesakeMathematics - Analysis of PDEshydrodynamic limitPhase (matter)FOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP][PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]sprays0101 mathematicsSettore MAT/07 - Fisica MatematicaVlasov-Stokes systemPhysicsNumerical Analysisgas mixture.010102 general mathematicsMSC Primary: 35Q20 35B25; Secondary: 82C40 76T15 76D07.Stokes flowBoltzmann equationAerosol010101 applied mathematicsClassical mechanicsModeling and SimulationBoltzmann constantKinetic theory of gasessymbolsVlasov-Stokes system Boltzmann equation Hydrodynamic limit Aerosols Sprays Gas mixtureaerosolsAnalysis of PDEs (math.AP)
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Derivation of Models for Thin Sprays from a Multiphase Boltzmann Model

2017

We shall review the validation of a class of models for thin sprays where a Vlasov type equation is coupled to an hydrodynamic equation of Navier–Stokes or Stokes type. We present a formal derivation of these models from a multiphase Boltzmann system for a binary mixture: under suitable assumptions on the collision kernels and in appropriate asymptotics (resp. for the two different limit models), we prove the convergence of solutions to the multiphase Boltzmann model to distributional solutions to the Vlasov–Navier–Stokes or Vlasov–Stokes system. The proofs are based on the procedure followed in Bardos et al. (J Stat Phys 63:323–344 (1991), [2]) and explicit evaluations of the coupling term…

Gas mixturePhysicsMathematics::Analysis of PDEsBinary numberType (model theory)Coupling (probability)Boltzmann equationBoltzmann equationSprayPhysics::Fluid Dynamicssymbols.namesakethin spraymultiphase boltzmann modelConvergence (routing)Boltzmann constantsymbolsKinetic theory of gasesHydrodynamic limitApplied mathematicsTwo-component systems Vlasov-Navier-Stokes systemStatistical physicsLimit (mathematics)Aerosol
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A DERIVATION OF THE VLASOV-NAVIER-STOKES MODEL FOR AEROSOL FLOWS FROM KINETIC THEORY

2016

This article proposes a derivation of the Vlasov-Navier-Stokes system for spray/aerosol flows. The distribution function of the dispersed phase is governed by a Vlasov-equation, while the velocity field of the propellant satisfies the Navier-Stokes equations for incompressible fluids. The dynamics of the dispersed phase and of the propellant are coupled through the drag force exerted by the propellant on the dispersed phase. We present a formal derivation of this model from a multiphase Boltzmann system for a binary gaseous mixture, involving the droplets/dust particles in the dispersed phase as one species, and the gas molecules as the other species. Under suitable assumptions on the colli…

MSC: 35Q20 35B25 (82C40 76T15 76D05)aerosolVlasov-Navier-Stokes systemGeneral Mathematics01 natural sciencesPhysics::Fluid DynamicsBoltzmann equationsymbols.namesakeMathematics - Analysis of PDEsThermal velocityPhase (matter)35Q20 35B25 (82C40 76T15 76D05)SpraysFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsSettore MAT/07 - Fisica MatematicaPhysicsPropellantAerosolsGas mixtureApplied Mathematics010102 general mathematicsMechanicsMass ratioBoltzmann equationAerosol010101 applied mathematicsDistribution functionsprayBoltzmann constantsymbolsHydrodynamic limitAnalysis of PDEs (math.AP)
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A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids

2019

A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained i…

Mathematics::Analysis of PDEsBinary number01 natural sciencesCompressible flow010305 fluids & plasmasPhysics::Fluid DynamicsBoltzmann equationSpraysymbols.namesakeIncompressible flow0103 physical sciences0101 mathematicsScalingAerosolSettore MAT/07 - Fisica MatematicaMathematicsGas mixtureApplied MathematicsVlasov-Euler systemHard spheresEuler system010101 applied mathematicsClassical mechanicsBoltzmann constantsymbolsKinetic theory of gasesHydrodynamic limit
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