Numerical High-Field Limits in Two-Stream Kinetic Models and 1D Aggregation Equations

DOI10.1137/151004653zbMath1457.65051OpenAlexW2275211603MaRDI QIDQ2790091

Nicolas Vauchelet, Laurent Gosse

Publication date: 2 March 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4f070e9afa9711200769cbb67f63250d75afdb12

zbMATH Keywords

Vlasov-Poisson-Fokker-Planck systemasymptotic-preserving and well-balanced schemehigh-field limitchemotaxis dynamicsduality measure solutionstwo-stream kinetic model

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Cell movement (chemotaxis, etc.) (92C17) Vlasov equations (35Q83) Fokker-Planck equations (35Q84)

Related Items (12)

Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport ⋮ Analysis and Simulation of Nonlinear and Nonlocal Transport Equations ⋮ Hydrodynamic singular regimes in \(1+1\) kinetic models and spectral numerical methods ⋮ Well-Balanced Schemes Based on Elementary Solutions for Kinetic Models of Ionized or Ultra-Relativistic Gas ⋮ Convergence analysis of upwind type schemes for the aggregation equation with pointy potential ⋮ Travelling Chemotactic Aggregates at Mesoscopic Scale and BiStability ⋮ The Vlasov--Poisson--Fokker--Planck System with Uncertainty and a One-dimensional Asymptotic Preserving Method ⋮ A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ⋮ Some examples of kinetic schemes whose diffusion limit is Il'in's exponential-fitting ⋮ \(\mathscr{L}\)-splines as diffusive limits of dissipative kinetic models ⋮ Diffusive limit of a two-dimensional well-balanced approximation to a kinetic model of chemotaxis ⋮ Diffusive Limit of a Two-Dimensional Well-Balanced Scheme for the Free Klein--Kramers Equation

Uses Software

• Chemotaxis

Cites Work

• Stringent error estimates for one-dimensional, space-dependent \(2\times 2\) relaxation systems
• Hydrodynamic singular regimes in \(1+1\) kinetic models and spectral numerical methods
• An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime
• Numerical simulation of a kinetic model for chemotaxis
• A remark on duality solutions for some weakly nonlinear scalar conservation laws
• Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
• Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes
• The structure of well-balanced schemes for Friedrichs systems with linear relaxation
• Derivation of hyperbolic models for chemosensitive movement
• The Filippov characteristic flow for the aggregation equation with mildly singular potentials
• Useful identities for half-space problems in linear transport theory
• Cattaneo models for chemosensitive movement
• Kinetic models for chemotaxis and their drift-diffusion limits
• Chemotaxis: from kinetic equations to aggregate dynamics
• A well-balanced scheme for kinetic models of chemotaxis derived from one-dimensional local forward-backward problems
• Stability of constant states and qualitative behavior of solutions to a one dimensional hyperbolic model of chemotaxis
• Diagonal defect measures, adhesion dynamics and Euler equation.
• A well-balanced scheme able to cope with hydrodynamic limits for linear kinetic models
• A deterministic particle method for the Vlasov-Fokker-Planck equation in one dimension
• Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms
• Combined Hermite spectral-finite difference method for the Fokker-Planck equation
• THE SET OF CONCENTRATION FOR SOME HYPERBOLIC MODELS OF CHEMOTAXIS
• Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
• Existence of solutions of the hyperbolic Keller-Segel model
• Stability Results for a Diffusion Equation With Functional Drift Approximating a Chemotaxis Model
• Separating variables in two-way diffusion equations
• On the Relationship Between Cell Balance Equations for Chemotactic Cell Populations
• One-dimensional transport equations with discontinuous coefficients
• Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients
• Convergence of a Difference Scheme for the Vlasov--Poisson--Fokker--Planck System in One Dimension
• Representation of Weak Limits and Definition of Nonconservative Products
• Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
• Some stochastic processes which arise from a model of the motion of a bacterium
• Computing Qualitatively Correct Approximations of Balance Laws
• Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients
• Numerical Methods for One-Dimensional Aggregation Equations
• A hyperbolic model of chemotaxis on a network: a numerical study
• High-field limit for the Vlasov-Poisson-Fokker-Planck system.

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