相关论文: Perfectly matched layers for the Boltzmann equatio…
A lattice Boltzmann (LB) theory, analytical characteristic integral (ACI) LB theory, is proposed in this paper. ACI LB theory takes Bhatnagar-Gross-Krook (BGK) Boltzmann equation as the exact kinetic equation behind Navier-Stokes continuum…
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time behavior - exponential decay to the global equilibrium - of the…
Ideal gases can be modeled by the Boltzmann equation from statistical physics. Instead of trying to track the position and velocity of a large number of gas molecules, it is possible to describe the particles with a particle distribution…
The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two…
Perfectly matched layers (PMLs) are formulated and applied to numerically solve nonlocal Helmholtz equations in one and two dimensions. In one dimension, we present the PML modifications for the nonlocal Helmholtz equation with general…
The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total…
A time domain system of equations is proposed to model elastic wave propagation in an unbounded two-dimensional anisotropic solid using perfectly matched layer (PML). Starting from a system of first-order frequency domain stress-velocity…
We propose fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and Bhatnagar-Gross-Krook (BGK) equations. The methods employ a sequence of small forward-Euler steps,…
The perfectly matched layers method is a well known truncation technique for its efficiency and convenience in numerical implementations of wave scattering problems in unbounded domains. In this paper, we study the convergence of the…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
Numerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional, nonlocal, and nonlinear collision integral. Over the past decade, the Fourier-Galerkin spectral method has become a popular…
We discuss how the Perfectly Matched Layer (PML) can be adapted to numerical simulations of nonlinear and matter wave systems, such as Bose-Einstein condensates. We also present some examples which illustrate the benefits of using the PML…
Bhatnagar-Gross-Krook (BGK) collision kernel is employed in the Boltzmann equation to formulate relativistic dissipative hydrodynamics. In this formulation, we find that there remains freedom of choosing a matching condition that affects…
The lattice Boltzmann method (LBM) is a popular numerical framework to investigate single and multiphase flow though porous media. For estimation of absolute permeability based on micro-tomographic images of the porous medium, the…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced [8, 17, 18]. These methods work in a satisfactory way either in rarefied or fluid regime. Moreover, because of the…
We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it…
The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. In [5], a linear convergence is proved for the…
Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong…