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The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is…

Numerical Analysis · Mathematics 2021-05-12 Dimitrios Mitsotakis , Hendrik Ranocha , David I. Ketcheson , Endre Süli

This work explores the feasibility of performing three-dimensional molecular gas dynamics simulations of hypersonic flows such as re-entry vehicles through directly solving the six-dimensional nonlinear Boltzmann equation closed with the…

Fluid Dynamics · Physics 2023-12-12 Tarik Dzanic , Luigi Martinelli

Based on the Hermite expansion of the distribution function, we introduce a Galerkin spectral method for the spatially homogeneous Boltzmann equation with the realistic inverse-power-law models. A practical algorithm is proposed to evaluate…

Numerical Analysis · Mathematics 2019-09-04 Yanli Wang , Zhenning Cai

We calculate in this work the Navier-Stokes transport coefficients from the Boltzmann equation for $d$-dimensional inelastic Maxwell models. By granular gas we mean here a low density system of identical spheres that lose a fraction of…

Statistical Mechanics · Physics 2015-06-18 Moisés G. Chamorro , Vicente Garzó , Francisco Vega Reyes

An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…

Computational Physics · Physics 2019-01-08 Wei Su , Peng Wang , Yonghao Zhang , Lei Wu

The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the…

Numerical Analysis · Mathematics 2019-10-02 Hongxu Chen , Qin Li , Jianfeng Lu

The multi-scale flow mechanism is crucial for force and heat loaded on near-space and reentry vehicles, the control of spacecraft by thrusters, the propelling and cooling of MEMS, etc. Since the continuum flow and rarefied flow often exist…

Computational Physics · Physics 2021-07-28 Sirui Yang , Sha Liu , Chengwen Zhong , Junzhe Cao , Congshan Zhuo

We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper…

Analysis of PDEs · Mathematics 2023-01-31 Ruo Li , Yichen Yang

We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in…

Numerical Analysis · Mathematics 2026-04-28 Klaas Willems , Axel Klar , Giovanni Russo , Giovanni Samaey , Sudarshan Tiwari

In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation…

Analysis of PDEs · Mathematics 2019-01-30 Esther S. Daus , Shi Jin , Liu Liu

The Direct Simulation Monte Carlo method is applied to solve the Boltzmann equation in the steady planar Couette flow for Maxwell molecules and hard spheres. Nonequilibrium boundary conditions based on the solution of the…

Statistical Mechanics · Physics 2007-05-23 J. M. Montanero , A. Santos , V. Garzó

Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…

Numerical Analysis · Mathematics 2026-02-19 Sudheer Mishra , Sundararajan Natarajan , E. Natarajan , Gianmarco Manzini

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the…

Fluid Dynamics · Physics 2018-12-26 Victor E. Ambrus , Victor Sofonea

The Boltzmann equation describes the detailed microscopic behaviour of a dilute gas, and represents the basis of the kinetic theory of gases. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a…

Mathematical Physics · Physics 2018-12-06 Armando Majorana

The Boltzmann equation becomes invalid as the size of gas molecules is comparable with the average intermolecular distance. A better description is provided by the Enskog collision operator, which takes into account the finite size of gas…

Fluid Dynamics · Physics 2023-01-25 S. Busuioc

Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first…

General Relativity and Quantum Cosmology · Physics 2023-05-30 Manuel R. Izquierdo , Lorenzo Pareschi , Borja Miñano , Joan Massó , Carlos Palenzuela

We present a quantitative comparison between two different Implicit-Explicit Runge-Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK…

Numerical Analysis · Mathematics 2025-10-23 Giuseppe Orlando , Sebastiano Boscarino , Giovanni Russo

A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…

Computational Physics · Physics 2013-11-19 Gian Pietro Ghiroldi , Livio Gibelli

A high-resolution Eulerian method for simulating high-speed polydisperse granular multiphase flows has been developed. The governing equations include a compressible gas that is coupled to mass-based moment equations for a polydisperse…

Fluid Dynamics · Physics 2026-03-17 Jacob W. Posey , Rodney O. Fox , Ryan W. Houim

This paper proposes a novel stochastic version of damped and regularized BFGS method for addressing the above problems.

Numerical Analysis · Mathematics 2019-12-11 H. Chen , H. C. Wu , S. C. Chan , W. H. Lam