562 research outputs found
DSMC-LBM mapping scheme for rarefied and non-rarefied gas flows
We present the formulation of a kinetic mapping scheme between the Direct
Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is
at the basis of the hybrid model used to couple the two methods in view of
efficiently and accurately simulate isothermal flows characterized by variable
rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we
propose ensures to accurately couple DSMC and LBM at a larger Kn number than
usually done in traditional hybrid DSMC-Navier-Stokes equation models. We show
the main steps of the mapping algorithm and illustrate details of the
implementation. Good agreement is found between the moments of the single
particle distribution function as obtained from the mapping scheme and from
independent LBM or DSMC simulations at the grid nodes where the coupling is
imposed. We also show results on the application of the hybrid scheme based on
a simpler mapping scheme for plane Poiseuille flow at finite Kn number.
Potential gains in the computational efficiency assured by the application of
the coupling scheme are estimated for the same flow.Comment: Submitted to Journal of Computational Scienc
Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo
In the present work, we present a novel numerical algorithm to couple the
Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann
equation with a finite volume like method for the solution of the Euler
equations. Recently we presented in [14],[16],[17] different methodologies
which permit to solve fluid dynamics problems with localized regions of
departure from thermodynamical equilibrium. The methods rely on the
introduction of buffer zones which realize a smooth transition between the
kinetic and the fluid regions. In this paper we extend the idea of buffer zones
and dynamic coupling to the case of the Monte Carlo methods. To facilitate the
coupling and avoid the onset of spurious oscillations in the fluid regions
which are consequences of the coupling with a stochastic numerical scheme, we
use a new technique which permits to reduce the variance of the particle
methods [11]. In addition, the use of this method permits to obtain estimations
of the breakdowns of the fluid models less affected by fluctuations and
consequently to reduce the kinetic regions and optimize the coupling. In the
last part of the paper several numerical examples are presented to validate the
method and measure its computational performances
A hybrid method for hydrodynamic-kinetic flow - Part I -A particle-gridmethod for reducing stochastic noise in kinetic regimes
In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime. The hybrid method is based on a first order splitting in time to separate the transport from the relaxation step. The transport step is solved by a deterministic scheme, while a hybrid DSMC-based method is used to solve the collision step. Such a hybrid scheme is based on splitting the solution in a collisional and a non-collisional part at the beginning of the collision step, and the DSMC method is used to solve the relaxation step for the collisional part of the solution only. This is accomplished by sampling only the fraction of particles candidate for collisions from the collisional part of the solution, performing collisions as in a standard DSMC method, and then projecting the particles back onto a velocity grid to compute a piecewise constant reconstruction for the collisional part of the solution. The latter is added to a piecewise constant reconstruction of the non-collisional part of the solution, which in fact remains unchanged during the relaxation step. Numerical results show that the stochastic noise is significantly reduced at large Knudsen numbers with respect to the standard DSMC method. Indeed in this algorithm, the particle scheme is applied only on the collisional part of the solution, so only this fraction of the solution is affected by stochastic fluctuations. But since the collisional part of the solution reduces as the Knudsen number increases, stochastic noise reduces as well at large Knudsen number
A Comparative Study of an Asymptotic Preserving Scheme and Unified Gas-kinetic Scheme in Continuum Flow Limit
Asymptotic preserving (AP) schemes are targeting to simulate both continuum
and rarefied flows. Many AP schemes have been developed and are capable of
capturing the Euler limit in the continuum regime. However, to get accurate
Navier-Stokes solutions is still challenging for many AP schemes. In order to
distinguish the numerical effects of different AP schemes on the simulation
results in the continuum flow limit, an implicit-explicit (IMEX) AP scheme and
the unified gas kinetic scheme (UGKS) based on Bhatnagar-Gross-Krook (BGk)
kinetic equation will be applied in the flow simulation in both transition and
continuum flow regimes. As a benchmark test case, the lid-driven cavity flow is
used for the comparison of these two AP schemes. The numerical results show
that the UGKS captures the viscous solution accurately. The velocity profiles
are very close to the classical benchmark solutions. However, the IMEX AP
scheme seems have difficulty to get these solutions. Based on the analysis and
the numerical experiments, it is realized that the dissipation of AP schemes in
continuum limit is closely related to the numerical treatment of collision and
transport of the kinetic equation. Numerically it becomes necessary to couple
the convection and collision terms in both flux evaluation at a cell interface
and the collision source term treatment inside each control volume
Hybrid discretizations of the Boltzmann equation for the dilute gas flow regime
New hybrid numerical model allows large scale flow simulations in high-tech production equipmen
General synthetic iterative scheme for nonlinear gas kinetic simulation of multi-scale rarefied gas flows
The general synthetic iteration scheme (GSIS) is extended to find the
steady-state solution of nonlinear gas kinetic equation, removing the
long-standing problems of slow convergence and requirement of ultra-fine grids
in near-continuum flows. The key ingredients of GSIS are that the gas kinetic
equation and macroscopic synthetic equations are tightly coupled, and the
constitutive relations in macroscopic synthetic equations explicitly contain
Newton's law of shear stress and Fourier's law of heat conduction. The
higher-order constitutive relations describing rarefaction effects are
calculated from the velocity distribution function, however, their
constructions are simpler than our previous work (Su et al. Journal of
Computational Physics 407 (2020) 109245) for linearized gas kinetic equations.
On the other hand, solutions of macroscopic synthetic equations are used to
inform the evolution of gas kinetic equation at the next iteration step. A
rigorous linear Fourier stability analysis in periodic system shows that the
error decay rate of GSIS can be smaller than 0.5, which means that the
deviation to steady-state solution can be reduced by 3 orders of magnitude in
10 iterations. Other important advantages of the GSIS are (i) it does not rely
on the specific form of Boltzmann collision operator and (ii) it can be solved
by sophisticated techniques in computational fluid dynamics, making it amenable
to large scale engineering applications. In this paper, the efficiency and
accuracy of GSIS is demonstrated by a number of canonical test cases in
rarefied gas dynamics.Comment: 25 pages, 17 figures; Version 3, major revision of text and
reformed/re-organized equations, added numerical analysis but numerical
results are not change
Mesoscopic simulation of diffusive contaminant spreading in gas flows at low pressure
Many modern production and measurement facilities incorporate multiphase
systems at low pressures. In this region of flows at small, non-zero Knudsen-
and low Mach numbers the classical mesoscopic Monte Carlo methods become
increasingly numerically costly. To increase the numerical efficiency of
simulations hybrid models are promising. In this contribution, we propose a
novel efficient simulation approach for the simulation of two phase flows with
a large concentration imbalance in a low pressure environment in the low
intermediate Knudsen regime. Our hybrid model comprises a lattice-Boltzmann
method corrected for the lower intermediate Kn regime proposed by Zhang et al.
for the simulation of an ambient flow field. A coupled event-driven
Monte-Carlo-style Boltzmann solver is employed to describe particles of a
second species of low concentration. In order to evaluate the model, standard
diffusivity and diffusion advection systems are considered.Comment: 9 pages, 8 figure
Towards an ultra efficient kinetic scheme. Part I: basics on the BGK equation
In this paper we present a new ultra efficient numerical method for solving
kinetic equations. In this preliminary work, we present the scheme in the case
of the BGK relaxation operator. The scheme, being based on a splitting
technique between transport and collision, can be easily extended to other
collisional operators as the Boltzmann collision integral or to other kinetic
equations such as the Vlasov equation. The key idea, on which the method
relies, is to solve the collision part on a grid and then to solve exactly the
transport linear part by following the characteristics backward in time. The
main difference between the method proposed and semi-Lagrangian methods is that
here we do not need to reconstruct the distribution function at each time step.
This allows to tremendously reduce the computational cost of the method and it
permits for the first time, to the author's knowledge, to compute solutions of
full six dimensional kinetic equations on a single processor laptop machine.
Numerical examples, up to the full three dimensional case, are presented which
validate the method and assess its efficiency in 1D, 2D and 3D
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