Study on gas kinetic unified algorithm for flows from rarefied transition to continuum

Li, Zhihui; Zhang, Hanxin

doi:10.1016/j.jcp.2003.08.022

Cited by 153 publications

(135 citation statements)

References 37 publications

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“…Despite the fact that the BKG equations are less complicated than the full Boltzmann equation, numerical techniques such as the lattice Boltzmann method or discrete velocity method [51][52][53][54] are typically required to solve them.…”

Section: A the Boltzmann Equationmentioning

confidence: 99%

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Sagert

Bauer

Colbry

et al. 2014

Journal of Computational Physics

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We introduce a massively parallelized test-particle based kinetic Monte Carlo code that is capable of modeling the phase space evolution of an arbitrarily sized system that is free to move in and out of the continuum limit. Our code combines advantages of the DSMC and the Point of Closest Approach techniques for solving the collision integral. With that, it achieves high spatial accuracy in simulations of large particle systems while maintaining computational feasibility. Using particle mean free paths which are small with respect to the characteristic length scale of the simulated system, we reproduce hydrodynamic behavior. To demonstrate that our code can retrieve continuum solutions, we perform a test-suite of classic hydrodynamic shock problems consisting of the Sod, the Noh, and the Sedov tests. We find that the results of our simulations which apply millions of test-particles match the analytic solutions well. In addition, we take advantage of the ability of kinetic codes to describe matter out of the continuum regime when applying large particle mean free paths. With that, we study and compare the evolution of shock waves in the hydrodynamic limit and in a regime which is not reachable by hydrodynamic codes.

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Section: A the Boltzmann Equationmentioning

confidence: 99%

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Sagert

Bauer

Colbry

et al. 2014

Journal of Computational Physics

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“…In this work, the velocity slip and temperature jump boundary conditions are treated as ordinary differential equations, at the neighborhood of the surface; also we concentrate on special case of a classical problem of low Reynolds number sphere flow. In the work by Li and Fu [5,6], the surface boundary conditions are treated with the gaskinetic theory, the results are related to the work here; however, they relied on numerical simulations, and used high Reynolds number flows over a sphere as a test case. There are experimental results available in the literature to validate their results, but the drag coefficients are different.…”

Section: Resultsmentioning

confidence: 99%

“…In the literature, there are some efforts to develop unified solvers (e.g. [5,6]), aiming to simulate the full Kn number flows, and several kinds of gaskinetic schemes for near continuum flows, e.g. [7].…”

Section: Introductionmentioning

confidence: 99%

Near continuum flows over a sphere

Cai

Sun

2015

Computers & Fluids

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a b s t r a c tIn this paper, the problem of near continuum gas flows over a sphere is investigated numerically. Three types of boundary conditions for the sphere surface are adopted: (1) non-slip and constant temperature surface; (2) velocity slip with considerations of velocity gradient, and temperature jump at the surface; and (3) velocity slip with considerations of both velocity and temperature gradients, as well as temperature jump at the surface. Navier-Stokes equations in a cylindrical coordinate system for compressible flows are adopted with the Roe numerical scheme. The numerical simulation results include coefficient distributions for surface pressure, friction, heat flux, velocity slip, temperature jump and total drag. The results are obtained with different free stream Knudsen and Mach numbers. Several conclusions include: (i) the third surface boundary condition does not create significant differences from the second type, (ii) however, an adoption of non-slip or a slip surface boundary condition can create significant differences in C f ; C q and C D .

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“…Many optimization problems such as searching for a local minimizer of function [1], the potential equations in the transonic regime of dense gases in gasdynamics [2] and the boundary value problems encountered in kinetic theory of gases [3], elasticity [4] and problems in other applied areas can be reduced to nonlinear equations. In general, to compute their roots we must drawn on to iterative methods.…”

Section: Introductionmentioning

confidence: 99%

One-point Newton-type iterative methods: A unified point of view

Cordero

Jordán

Torregrosa

2015

Journal of Computational and Applied Mathematics

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In this paper, an unified point of view that include the most of one-point Newton-type iterative methods for solving nonlinear equations is introduced. A simple idea to design iterative methods with quadratic or cubic convergence is also described. This idea is extended to construct one-point iterative methods of order four. In addition, several numerical examples are given to illustrate and compare different known methods and some ones introduced by using this unifying idea.

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Study on gas kinetic unified algorithm for flows from rarefied transition to continuum

Cited by 153 publications

References 37 publications

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Near continuum flows over a sphere

One-point Newton-type iterative methods: A unified point of view

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