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We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…
In this work, we present a family of time and space high order finite volume schemes for the solution of the full Boltzmann equation. The velocity space is approximated by using a discrete ordinate approach while the collisional integral is…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…
In this paper, a detailed analysis on normal modes of the linearized Hermite collision operator is presented, which follows from linearizing spin Boltzmann equation for massive fermions proposed in \cite{Weickgenannt:2021cuo} with the…
In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is…
We propose an adaptive Hermite spectral method for the three-dimensional velocity space of the Boltzmann equation guided by a newly developed frequency indicator. For the homogeneous problem, the indicator is defined by the contribution of…
It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the first flux reconstruction method for high-order Boltzmann…
The lattice Boltzmann (LB) method intrinsically links to the Boltzmann equation with the Bhatnagar-Gross-Krook collision operator; however, it has been questioned to be able to simulate noncontinuum bounded gas flows at the micro and…
Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB…
The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…
This paper develops a modified version of the Boltzmann equation for micro-scale particulate flow with capture and diffusion that describes the colloidal-suspension-nano transport in porous media. An equivalent sink term is introduced into…
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex…
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic methods, the Fourier-Galerkin spectral method stands out for…
We present a numerical method for the velocity-space, spatially homogeneous, collisional Boltzmann equation for electron transport in low-temperature plasma (LTP) conditions. Modeling LTP plasmas is useful in many applications, including…
We study the structure of a shock wave for a two-, three- and four-component gas mixture on the basis of numerical solution of the Boltzmann equation for the model of hard sphere molecules. For the evaluation of collision integrals we use…
Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order…
A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the…
In this paper, we first extend the micro-macro decomposition method for multiscale kinetic equations from the BGK model to general collisional kinetic equations, including the Boltzmann and the Fokker-Planck Landau equations. The main idea…
In this paper we study multivariate kinetic-type equations in a general setup, which includes in particular the spatially homogeneous Boltzmann equation with Maxwellian molecules, both with elastic and inelastic collisions. Using a…
A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based…