Related papers: On deterministic approximation of the Boltzmann eq…
The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
The rigorous justification of the hydrodynamic limits of kinetic equations in bounded domains has been actively investigated in recent years. In spite of the progress for the diffuse-reflection boundary case, the more challenging in-flow…
Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The…
In the paper, assuming that the motion of rarefied gases in a bounded domain is governed by the angular cutoff Boltzmann equation with diffuse reflection boundary, we study the effects of both soft intermolecular interaction and…
We introduce a fast Fourier spectral method to compute linearized collision operators of the Boltzmann equation for variable hard-sphere gases. While the state-of-the-art method provides a computational cost O(MN^4 log N), with N being the…
Let rarefied gas be confined in an infinite layer with diffusely reflecting boundaries that are isothermal and non-moving. The initial-boundary value problem on the nonlinear Boltzmann equation governing the rarefied gas flow in such…
The parallel solver of the general synthetic iterative scheme (GSIS), as recently developed by Zhang \textit{et. al.} in Comput. Fluids 281 (2024) 106374, is an efficient method to find the solution of the Boltzmann equation…
Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number $\epsilon\rightarrow 0^+$. Using the Hilbert expansion, we rigorously…
This manuscript derives adjoint equations for the numerical solution of the spatially inhomogeneous Boltzmann equation using Direct Simulation Monte Carlo (DSMC). The formulation accounts for spatial transport and a range of boundary…
We present a new deterministic approach for the solution of the Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in velocity space. In the new approach the collision operator has the form of a bilinear…
We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to…
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
In this paper we present a numerical method for the Boltzmann equation. It is a spectral discretization in the velocity and a discontinuous Galerkin discretization in physical space. To obtain uniform approximation properties in the mach…
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…
A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the…
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…