120 research outputs found
Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium
Hypersonic flow around a vehicle in near space flight is associated with
multiscale non-equilibrium physics at a large variation of local Knudsen number
from the leading edge highly compressible flow to the trailing edge particle
free transport. To accurately capture the solution in all flow regimes from the
continuum Navier-Stokes solution to the rarefied gas dynamics in a single
computation requires genuinely multiscale method. The unified gas-kinetic
wave-particle (UGKWP) method targets on the simulation of such a multicale
transport. Due to the wave-particle decomposition, the dynamics in the
Navier-Stokes wave and kinetic particle transport has been unified
systematically and efficiently under the unified gas-kinetic scheme (UGKS)
framework. In this study, the UGKWP method with the non-equilibrium among
translation, rotation and vibration modes, is developed based on a multiple
temperature relaxation model. The real gas effect for high speed flow in
different flow regimes has been properly captured. Numerical tests, including
Sod tube, normal shock structure, hypersonic flow around two-dimensional
cylinder and three-dimensional flow around a sphere and space vehicle, have
been conducted to validate the UGKWP method. In comparison with the discrete
velocity method (DVM)-based Boltzmann solver and particle-based direct
simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable
advantages in terms of computational efficiency, memory reduction, and
automatic recovering of multiscale solution
Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations
With wave-particle decomposition, a unified gas-kinetic wave-particle (UGKWP)
method has been developed for the multiscale flow simulations. The UGKWP method
captures the transport process in all flow regimes without kinetic solver's
constraint on the numerical mesh size and time step being less than the
particle mean free path and collision time. In the current UGKWP method, the
cell's Knudsen number, defined as the ratio of collision time to numerical time
step, is used to distribute the components in the wave-particle decomposition.
However, the adaptation of particle in UGKWP is mainly for the capturing of the
non-equilibrium transport, and the cell's Knudsen number alone is not enough to
identify the non-equilibrium state. For example, in the equilibrium flow regime
with a Maxwellian distribution function, even at a large cell's Knudsen number,
the flow evolution can be still modelled by the Navier-Stokes solver.
Therefore, to further improve the efficiency, an adaptive UGKWP (AUGKWP) method
will be developed with the introduction of an additional local flow variable
gradient-dependent Knudsen number. As a result, the wave-particle decomposition
in UGKWP will be determined by both cell's and gradient's Knudsen numbers, and
the particle in UGKWP is solely used to capture the non-equilibrium flow
transport. The AUGKWP becomes much more efficient than the previous one with
the cell's Knudsen number only in the determination of wave-particle
composition. Many numerical tests, including Sod tube, shock structure, flow
around a cylinder, flow around a reentry capsule, and an unsteady nozzle plume
flow, have been conducted to validate the accuracy and efficiency of AUGKWP.
Compared with the original UGKWP, the AUGKWP achieves the same accuracy but has
advantages in memory reduction and computational efficiency in the simulation
for the flow with the co-existing of multiple regimes.Comment: arXiv admin note: substantial text overlap with arXiv:2211.1292
A direct unified wave-particle method for simulating non-equilibrium flows
In this work, the Navier-Stokes (NS) solver is combined with the Direct
simulation Monte Carlo (DSMC) solver in a direct way, under the wave-particle
formulation [J. Comput. Phys. 401, 108977 (2020)]. Different from the classical
domain decomposition method with buffer zone for overlap, in the proposed
direct unified wave-particle (DUWP) method, the NS solver is coupled with DSMC
solver on the level of algorithm. Automatically, in the rarefied flow regime,
the DSMC solver leads the simulation, while the NS solver leads the continuum
flow simulation. Thus advantages of accuracy and efficiency are both taken. At
internal flow regimes, like the transition flow regime, the method is accurate
as well because a kind of mesoscopic modeling is proposed in this work, which
gives the DUWP method the multi-scale property. Specifically, as to the
collision process, at , it is supposed that only single collision
happens, and the collision term of DSMC is just used. At , it is
derived that of particles should experience multiple
collisions, which will be absorbed into the wave part and calculated by the NS
solver. Then the DSMC and NS solver can be coupled in a direct and simple way,
bringing about multi-scale property. The governing equation is derived and
named as multi-scale Boltzmann equation. Different from the original
wave-particle method, in the proposed DUWP method, the wave-particle
formulation is no more restricted by the Boltzmann-BGK type model and the
enormous research findings of DSMC and NS solvers can be utilized into much
more complicated flows, like the thermochemical non-equilibrium flow. In this
work, one-dimensional cases in monatomic argon gas are preliminarily tested,
such as shock structures and Sod shock tubes
Efficient parallel solver for high-speed rarefied gas flow using GSIS
Recently, the general synthetic iterative scheme (GSIS) has been proposed to
find the steady-state solution of the Boltzmann equation in the whole range of
gas rarefaction, where its fast-converging and asymptotic-preserving properties
lead to the significant reduction of iteration numbers and spatial cells in the
near-continuum flow regime. However, the efficiency and accuracy of GSIS has
only been demonstrated in two-dimensional problems with small numbers of
spatial cell and discrete velocities. Here, a large-scale parallel computing
strategy is designed to extend the GSIS to three-dimensional high-speed flow
problems. Since the GSIS involves the calculation of the mesoscopic kinetic
equation which is defined in six-dimensional phase-space, and the macroscopic
high-temperature Navier-Stokes-Fourier equations in three-dimensional physical
space, the proper partition of the spatial and velocity spaces, and the
allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys
to improving the overall computational efficiency. These factors are
systematically tested to achieve optimal performance, up to 100 billion spatial
and velocity grids. For hypersonic flows around the Apollo reentry capsule, the
X38-like vehicle, and the space station, our parallel solver can get the
converged solution within one hour
Competition of natural convection and thermal creep in a square enclosure
Although natural convection and thermal creep have been well recognized in the continuum and rarefied regimes, respectively, the study of the competition of them in a wide flow regime is very scarce. From a theoretical point of view, natural convection can be described by Navier–Stokes–Fourier (NSF) equations at the macroscopic level, while thermal creep needs descriptions at the molecular level. Therefore, it is quite challenging to capture these two effects simultaneously. In this work, we employ the unified stochastic particle Bhatnagar–Gross–Krook (USP-BGK) method to investigate thermally driven gas flow in a square enclosure. The simulation results obtained by the USP-BGK method are validated by comparing to those from NSF solutions and direct simulation Monte Carlo method for the continuum and transitional regimes, respectively. We find that the flow patterns in the whole flow regime cannot be determined by just one nondimensional parameter, i.e., the Rayleigh number (Ra), but needs two nondimensional parameters, i.e., the Knudsen number (Kn) and the Froude number (Fr), or Kn and Ra. Specifically, small Knudsen and Froude numbers tend to generate natural convection, while large Knudsen and Froude numbers tend to cause thermal creep. Moreover, our simulation results and analyses demonstrate that when Kn 0.28, or equivalently, L/L* > 1.0, where L is the characteristic length of the system and L* is the equivalent characteristic length of molecules. These findings provide useful guidance for better understanding of the complex gas flows resulting from the competition of natural convection and thermal creep under microscale or low-density conditions such as on Mars
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