Half-space kinetic equations with general boundary conditions

  title={Half-space kinetic equations with general boundary conditions},
  author={Qin Li and J. Lu and W. Sun},
  journal={Math. Comput.},
  • Qin Li, J. Lu, W. Sun
  • Published 2017
  • Mathematics, Physics, Computer Science
  • Math. Comput.
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary conditions. As in [LLS14], the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method… Expand
Validity and Regularization of Classical Half-Space Equations
Recent result (Wu and Guo in Commun Math Phys 336(3):1473–1553, 2015) has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture theExpand
A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer
A full domain numerical solver is developed with a domain-decomposition approach, where the Euler solver and kinetic solver are applied on the appropriate subdomains and connected via the half-space solver. Expand
Kinetic Layers and Coupling Conditions for Macroscopic Equations on Networks I: The Wave Equation
A new approximate method for the solution of kinetic half-space problems is derived and used for the determination of the coupling conditions, and numerical comparisons between the solutions of the macroscopic equation with different coupling conditions and the kinetic solution are presented. Expand
Asymptotic preserving and time diminishing schemes for rarefied gas dynamic
In this work, we introduce a new class of numerical schemes for rarefied gas dynamic problems described by collisional kinetic equations. The idea consists in reformulating the problem using aExpand
An Asymptotic Preserving Method for Transport Equations with Oscillatory Scattering Coefficients
  • Qin Li, J. Lu
  • Computer Science, Mathematics
  • Multiscale Model. Simul.
  • 2017
A numerical scheme for transport equations with oscillatory periodic scattering coefficients that captures the homogenization limit as the length scale of the scattering coefficient goes to zero and is analyzed in the asymptotic regime, as well as validated numerically. Expand
A Nonlinear Discrete Velocity Relaxation Model For Traffic Flow
We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit forExpand
Kinetic layers and coupling conditions for nonlinear scalar equations on networks
We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kineticExpand
Error analysis of an asymptotic preserving dynamical low-rank integrator for the multi-scale radiative transfer equation
This work performs an error analysis for a dynamical low-rank algorithm applied to a classical model in kinetic theory, namely the radiative transfer equation, and proves that the scheme dynamically and automatically captures the low rank structure of the solution, and preserves the fluid limit on the numerical level. Expand
Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit
Dynamical low-rank algorithms are a class of numerical methods that compute lowrank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensionalExpand
Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains
Consider the steady neutron transport equation with diffusive boundary condition. In Wu and Guo (Commun Math Phys 336:1473–1553, 2015) and Wu et al. (J Stat Phys 165:585–644, 2016), it was discoveredExpand


A convergent method for linear half-space kinetic equations
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in aExpand
On half-space problems for the linearized discrete Boltzmann equation
In this paper we study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for the discrete Boltzmann equation. The discrete Boltzmann equation reducesExpand
A classification of well‐posed kinetic layer problems
In the first part of this paper, we study the half space boundary value problem for the Boltzmann equation with an incoming distribution, obtained when considering the boundary layer arising in theExpand
The nonlinear boundary layer to the Boltzmann equation with mixed boundary conditions for hard potentials
In this paper, the existence of boundary layer solutions to the Boltzmann equation for hard potential with mixed boundary condition, i.e., a linear combination of Dirichlet boundary condition andExpand
A numerical method for computing asymptotic states and outgoing distributions for kinetic linear half-space problems
Linear half-space problems can be used to solve domain decomposition problems between Boltzmann and aerodynamic equations. A new fast numerical method computing the asymptotic states and outgoingExpand
Existence of solutions of weakly non-linear half-space problems for the general discrete velocity (with arbitrarily finite number of velocities) model of the Boltzmann equation are studied. TheExpand
We present a rigorous variational framework for the analysis and discretization of the radiative transfer equation. Existence and uniqueness of weak solutions are established under rather generalExpand
Nonlinear Boundary Layers of the Boltzmann Equation
The Dirichlet problem of the nonlinear Boltzmann equation in the half-space arises in the analysis of the kinetic boundary layer, the condensation-evaporation problem and other problems related toExpand
Errata: Computation of the asymptotic states for linear half space kinetic problems
Abstract A spectral numerical scheme computing the asymptotic states for linear half space problems is described in the case of a simple transport equation and the linearized Bhatnagar-Gross-KrookExpand
Boundary Singularity for Thermal Transpiration Problem of the Linearized Boltzmann Equation
We study the boundary singularity of the fluid velocity for the thermal transpiration problem in the kinetic theory. Logarithmic singularity has been demonstrated through the asymptotic andExpand