307 research outputs found
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
A Nonlinear Multigrid Steady-State Solver for Microflow
We develop a nonlinear multigrid method to solve the steady state of
microflow, which is modeled by the high order moment system derived recently
for the steady-state Boltzmann equation with ES-BGK collision term. The solver
adopts a symmetric Gauss-Seidel iterative scheme nested by a local Newton
iteration on grid cell level as its smoother. Numerical examples show that the
solver is insensitive to the parameters in the implementation thus is quite
robust. It is demonstrated that expected efficiency improvement is achieved by
the proposed method in comparison with the direct time-stepping scheme
A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects
This paper collects the efforts done in our previous works [P. Degond, S.
Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic
Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L.
Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J.
Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L.
Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects,
SIAM Multi. Model. Sim. 5(3), 940--979 (2006)] to build a robust multiscale
kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems
which present non equilibrium localized regions that can move, merge, appear or
disappear in time. The main ingredients of the present work are the followings
ones: a fluid model is solved in the whole domain together with a localized
kinetic upscaling term that corrects the fluid model wherever it is necessary;
this multiscale description of the flow is obtained by using a micro-macro
decomposition of the distribution function [P. Degond, J.G. Liu, L. Mieussens,
Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi.
Model. Sim. 5(3), 940--979 (2006)]; the dynamic transition between fluid and
kinetic descriptions is obtained by using a time and space dependent transition
function; to efficiently define the breakdown conditions of fluid models we
propose a new criterion based on the distribution function itself. Several
numerical examples are presented to validate the method and measure its
computational efficiency.Comment: 34 page
Multi-scale semi-Lagrangian lattice Boltzmann method
We present a multi-scale lattice Boltzmann scheme, which adaptively refines
particles' velocity space. Different velocity sets, i.e., higher- and
lower-order lattices, are consistently and efficiently coupled, allowing us to
use the higher-order lattice only when and where needed. This includes regions
of either high Mach number or high Knudsen number. The coupling procedure of
different lattices consists of either projection of the moments of the
higher-order lattice onto the lower-order lattice or lifting of the lower-order
lattice to the higher-order velocity space. Both lifting and projection are
local operations, which enable a flexible adaptive velocity set. The proposed
scheme can be formulated both in a static and an optimal, co-moving reference
frame, in the spirit of the recently introduced Particles on Demand method. The
multi-scale scheme is first validated through a convected athermal vortex and
also studied in a jet flow setup. The performance of the proposed scheme is
further investigated through the shock structure problem and a high Knudsen
Couette flow, typical examples of highly non-equilibrium flows in which the
order of the velocity set plays a decisive role. The results demonstrate that
the proposed multi-scale scheme can operate accurately, with flexibility in
terms of the underlying models and with reduced computational requirements
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