Numerical methods for kinetic equations (Q4683916)

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scientific article; zbMATH DE number 6944159

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English	Numerical methods for kinetic equations	scientific article; zbMATH DE number 6944159

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scholarly article

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Numerical methods for kinetic equations (English)

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Giacomo Dimarco

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Lorenzo Pareschi

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publication date

26 September 2018

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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The heterogeneous multiscale method

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A hybrid method for hydrodynamic-kinetic flow. I: A particle-grid method for reducing stochastic noise in kinetic regimes

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A hybrid method for hydrodynamic-kinetic flow. II: Coupling of hydrodynamic and kinetic models

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Wavelet approximations of a collision operator in kinetic theory

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Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

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Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

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Variance reduction for Monte Carlo solutions of the Boltzmann equation

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Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations

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Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation

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From a class of kinetic models to the macroscopic equations for multicellular systems in biology

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Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics

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Convergence of a Semi-Lagrangian Scheme for the One-Dimensional Vlasov--Poisson System

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Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space

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A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems

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Fast deterministic method of solving the Boltzmann equation for hard spheres

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Numerical solution of the Boltzmann equation using a fully conservative difference scheme based on the fast fourier transform

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On some properties of kinetic and hydrodynamic equations for inelastic interactions.

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Fast Multipole Method for Multivariable Integrals

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Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works

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Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit

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Equilibrium schemes for scalar conservation laws with stiff sources

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A BGK model for small Prandtl number in the Navier-Stokes approximation

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Coupling Boltzmann and Navier-Stokes equations by friction

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Shock Structure in a Simple Discrete Velocity Gas

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A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics

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Numerical Analysis of Conservative and Entropy Schemes for the Fokker--Planck--Landau Equation

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An asymptotic preserving scheme for hydrodynamics radiative transfer models. Numerics for radiative transfer

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Regularized Boltzmann operators

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A low diffusion particle method for simulating compressible inviscid flows

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A hybrid particle approach for continuum and rarefied flow simulation

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The fluid dynamic limit of the nonlinear boltzmann equation

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A Hybrid Method for Accelerated Simulation of Coulomb Collisions in a Plasma

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Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation

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Convergence of an adaptive semi-Lagrangian scheme for the Vlasov-Poisson system

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Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models

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2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods

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Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

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The Boltzmann equation and its applications

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The mathematical theory of dilute gases

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Enhanced Convergence Estimates for Semi-Lagrangian Schemes Application to the Vlasov--Poisson Equation

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Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations

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Numerical solution of Boltzmann's equation

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Advanced numerical approximation of nonlinear hyperbolic equations. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C. I. M. E.) held in Cetraro, Italy, June 23--28, 1997

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An Algorithm for the Machine Calculation of Complex Fourier Series

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On a kinetic model for a simple market economy

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Numerical Passage from Kinetic to Fluid Equations

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Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles

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An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: diffusion and high-field scaling limits

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Asymptotic preserving schemes for highly oscillatory Vlasov-Poisson equations

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Conservative semi-Lagrangian schemes for Vlasov equations

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A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

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Asymptotic-Preserving Schemes for Fluid Models of Plasmas

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Fluid simulations with localized Boltzmann upscaling by direct simulation Monte-Carlo

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A moving interface method for dynamic kinetic-fluid coupling

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Large deformation of liquid capsules enclosed by thin shells immersed in the fluid

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The moment-guided Monte Carlo method

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A smooth transition model between kinetic and hydrodynamic equations

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Modeling and computational methods for kinetic equations

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ABOUT THE SPLITTING ALGORITHM FOR BOLTZMANN AND B.G.K. EQUATIONS

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Commutateurs de certains semi-groupes holomorphes et applications aux directions alternées

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The moment guided Monte Carlo method for the Boltzmann equation

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Towards an ultra efficient kinetic scheme. I: Basics on the BGK equation

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Towards an ultra efficient kinetic scheme. II: The high order case

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Hybrid multiscale methods. I: Hyperbolic relaxation problems

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Hybrid Multiscale Methods II. Kinetic Equations

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Fluid Solver Independent Hybrid Methods for Multiscale Kinetic Equations

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Exponential Runge–Kutta Methods for Stiff Kinetic Equations

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High order asymptotic-preserving schemes for the Boltzmann equation

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Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations

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Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors

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Lattice points on circles and discrete velocity models for the Boltzmann equation

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A numerical solution to the Vlasov equation

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Convergence of a Finite Volume Scheme for the Vlasov--Poisson System

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On Deterministic Approximation of the Boltzmann Equation in a Bounded Domain

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A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources

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An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation

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Analysis of spectral methods for the homogeneous Boltzmann equation

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High order numerical methods for the space non-homogeneous Boltzmann equation.

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A rescaling velocity method for dissipative kinetic equations. Applications to granular media

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Semilagrangian schemes applied to moving boundary problemsfor the BGK model of rarefied gas dynamics

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A numerical scheme for the quantum Boltzmann equation with stiff collision terms

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Solving the Boltzmann Equation in <i>N</i> log<sub>2</sub><i>N</i>

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Accurate numerical methods for the collisional motion of (heated) granular flows

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Conservative numerical schemes for the Vlasov equation

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Relaxation Schemes for Nonlinear Kinetic Equations

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A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

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Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

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Shock and Boundary Structure Formation by Spectral-Lagrangian Methods for the Inhomogeneous Boltzmann Transport Equation

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A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization

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Numerical approximation of hyperbolic systems of conservation laws

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The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels

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Well-balanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension

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Computing Qualitatively Correct Approximations of Balance Laws

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An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations

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Space Localization and Well-Balanced Schemes for Discrete Kinetic Models in Diffusive Regimes

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A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations

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A spectral method of solving Boltzmann's kinetic equation numerically

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\(L^ p\)-estimates for the nonlinear spatially homogeneous Boltzmann equation

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From particle to kinetic and hydrodynamic descriptions of flocking

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An asymptotic-preserving semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation

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A discontinuous Galerkin method for the Vlasov-Poisson system

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Averaged kinetic models for flows on unstructured networks

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Exponential integrators

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Low-variance deviational simulation Monte Carlo

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A low-variance deviational simulation Monte Carlo for the Boltzmann equation

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A fast spectral algorithm for the quantum Boltzmann collision operator

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Numerical solution of the Boltzmann equation on the uniform grid

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Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms

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Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations

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Fully-discrete numerical transfer in diffusive regimes

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Numerical schemes for hyperbolic conservation laws with stiff relaxation terms

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A BGK‐penalization‐based asymptotic‐preserving scheme for the multispecies Boltzmann equation

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Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes

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Asymptotic-Preserving Numerical Schemes for the Semiconductor Boltzmann Equation Efficient in the High Field Regime

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The relaxation schemes for systems of conservation laws in arbitrary space dimensions

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A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation

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A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion

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Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations

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Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations

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Additive Runge-Kutta schemes for convection-diffusion-reaction equations

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An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit

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Asymptotic-Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations

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Enskog-like kinetic models for vehicular traffic

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Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

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Numerical solutions of the Boltzmann equation: Comparison of different algorithms

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Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit

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Time evolution of large classical systems

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Relaxed micro-macro schemes for kinetic equations

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Micro-Macro Schemes for Kinetic Equations Including Boundary Layers

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Implicit Schemes for the Fokker--Planck--Landau Equation

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A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

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Moment closure hierarchies for kinetic theories.

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Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy

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Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II

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Boltzmann equation: micro-macro decompositions and positivity of shock profiles

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A numerical model of the Boltzmann equation related to the discontinuous Galerkin method

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Fast conservative and entropic numerical methods for the boson Boltzmann equation

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An Approximate Newton Method for the Solution of the Basic Semiconductor Device Equations

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Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations

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DISCRETE VELOCITY MODEL AND IMPLICIT SCHEME FOR THE BGK EQUATION OF RAREFIED GAS DYNAMICS

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Convergence of a discrete-velocity model for the Boltzmann-BGK equation

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Convergence of discrete-velocity schemes for the Boltzmann equation

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Fast methods for the Boltzmann collision integral

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Fast algorithms for computing the Boltzmann collision operator

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Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

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Numerical schemes for kinetic equations in diffusive regimes

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Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation

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Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit

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Mathematical modeling of collective behavior in socio-economic and life sciences

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Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation

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Multidimensional Farey partitions

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Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules

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A Consistency Result for a Discrete-Velocity Model of the Boltzmann Equation

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A new consistent discrete-velocity model for the Boltzmann equation

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An implicit Monte Carlo method for rarefied gas dynamics. I: The space homogeneous case

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A Fourier spectral method for homogeneous boltzmann equations

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Asymptotic preserving Monte Carlo methods for the Boltzmann equation

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Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator

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On the stability of spectral methods for the homogeneous Boltzmann equation

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Time Relaxed Monte Carlo Methods for the Boltzmann Equation

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Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation

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Fast spectral methods for the Fokker-Planck-Landau collision operator.

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Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit

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Adaptive and Recursive Time Relaxed Monte Carlo Methods for Rarefied Gas Dynamics

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Global existence to the BGK model of Boltzmann equation

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Boltzmann Type Schemes for Gas Dynamics and the Entropy Property

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Implicit-explicit schemes for BGK kinetic equations

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Microscopically implicit-macroscopically explicit schemes for the BGK equation

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An acceleration procedure for discrete velocity approximation of the Boltzmann collision operator

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On a conservative polar discretization of the Boltzmann equation

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Direct simulation methods for compressible inviscid ideal-gas flow

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Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system

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A robust numerical method for the R13 equations of rarefied gas dynamics: application to lid driven cavity

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Analysis of a new class of forward semi-Lagrangian schemes for the 1D Vlasov Poisson equations

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A stochastic weighted particle method for the Boltzmann equation

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Simulation of rare events by the stochastic weighted particle method for the Boltzmann equa\-tion.

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A direct method for solving the Boltzmann equation

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Convergence of a Semi-Lagrangian Scheme for the BGK Model of the Boltzmann Equation

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Direct coupling of fluid and kinetic equations

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High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

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Efficient implementation of essentially nonoscillatory shock-capturing schemes. II

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A numerical solution of boltzmann's equation

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Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules

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The semi-Lagrangian method for the numerical resolution of the Vlasov equation

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On the Construction and Comparison of Difference Schemes

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Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.

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Coupling of the Boltzmann and Euler equations with automatic domain decomposition

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An adaptive domain decomposition procedure for Boltzmann and Euler equations

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Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I

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Acceleration Schemes of the Discrete Velocity Method: Gaseous Flows in Rectangular Microchannels

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Deterministic numerical solutions of the Boltzmann equation using the fast spectral method

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A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method

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full work available at URL

https://doi.org/10.1017/s0962492914000063

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Identifiers

zbMATH Open document ID

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10.1017/S0962492914000063

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:4683916

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