Related papers: Local discrete velocity grids for deterministic ra…
Most of deterministic solvers for rarefied gas dynamics use discrete velocity (or discrete ordinate) approximations of the distribution function on a Cartesian grid. This grid must be sufficiently large and fine to describe the distribution…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity…
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian…
The gas-kinetic scheme (GKS) provides high computational efficiency and accuracy for continuum flow simulations but is unable to reliably capture rarefaction effects. In contrast, although the discrete velocity method (DVM) is better suited…
Continuum computational kinetic plasma models evolve the distribution function of a plasma species $f_s$ on a phase-space grid over time. In many problems of interest the distribution function has limited extent in velocity space; hence,…
In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. Although various versions of DVM have been developed, their performance, in terms of accuracy and…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…
The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial…
In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified…
In this paper, the driven cavity problem was solved using finite difference scheme in stream function-vorticity formulation. A variable grid is adopted to capture more details and information in the area nearby the wall. The Navier-Stokes…
Ray effect usually appears in the radiative transfer when using discrete ordinates method (DOM) in the simulations. The cause and remedy for the ray effect have been intensively investigated in the radiation community. For rarefied gas…
In this series of works, we develop a discrete-velocity-direction model (DVDM) with collisions of BGK-type for simulating rarefied flows. Unlike the conventional kinetic models (both BGK and discrete-velocity models), the new model…
Both discrete and continuum models have been widely used to study rapid granular flow, discrete model is accurate but computationally expensive, whereas continuum model is computationally efficient but its accuracy is doubtful in many…
I give an overview of rare event simulation techniques to generate dynamical pathways across high free energy barriers. The methods on which I will concentrate are the reactive flux approach, transition path sampling, (replica-exchange)…
Discrete unified gas-kinetic scheme (DUGKS) is a multi-scale numerical method for flows from continuum limit to free molecular limit, and is especially suitable for the simulation of multi-scale flows, benefiting from its multi-scale…
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…
This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…
Rooted from the gas kinetics, the lattice Boltzmann method is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate the rarefied gas flow beyond the Navier-Stokes level, either by using the…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…