Search results for " 35Q20"

showing 3 items of 3 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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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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Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data

2013

The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…

ta113Applied MathematicsGeneral MathematicsOperator (physics)ta111010102 general mathematicsMathematical analysisMicrolocal analysisNumerical Analysis (math.NA)Inverse problem01 natural sciences35R30 (Primary) 35S05 35R09 35Q20 92C55Neumann series010101 applied mathematicsSobolev spaceMathematics - Analysis of PDEsRadiative transferFOS: MathematicsGravitational singularityMathematics - Numerical Analysis0101 mathematicsAnisotropyMathematicsAnalysis of PDEs (math.AP)
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