497 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
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Rarefied flow between plates of finite length via the coupling approach
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The coexistence of rarefied continuum flow regime areas and relatively small elements in which rarefaction effects become important is a typical feature of many complex gas flows micro systems. In rarefied domains, the mean free path of gas molecules is comparable or larger than a characteristic scale of the system. These domains are naturally described by kinetic equation for the velocity distribution function, which involve a considerable effort in terms of CPU time and memory requirements, due to the discretization in both physical and velocity space. The continuum domains are best described by the fluid Navier Stokes (NS) equations in terms of average flow velocity, gas density and temperature. These equations are more efficient, but less accurate in critical rarefied areas. Thus, the development of hybrid solver combining kinetic and continuum models is of great interest especially for applications range from gas flows in micro systems to the aerospace applications, such as high altitude flights. The pressure–driven gas flow of rarified monatomic gas through a two-dimensional short microchannel is considered using hybrid solver. The calculations have been carried out for pressure ratios 0.1, 0.5 and 0.9 and fixed relatively large Knudsen number. The applicability of the solver is discussed via comparison with the kinetic and NS solutions.The European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS no 215504
A global adaptive velocity space for general discrete velocity framework in predictions of rarefied and multi-scale flows
The rarefied flow and multi-scale flow are crucial for the aerodynamic design
of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete
velocity space, the Boltzmann method, such as the discrete velocity method and
unified methods, can capture complex and non-equilibrium velocity distribution
functions (VDFs) and describe flow behaviors exactly. However, the extremely
steep slope and high concentration of the gas VDFs in a local particle velocity
space make it very difficult for the Boltzmann method with structured velocity
space to describe high speed flow. Therefore, the adaptive velocity space (AVS)
is required for the Boltzmann solvers to be practical in complex rarefied flow
and multi-scale flow. This paper makes two improvements to the AVS approach,
which is then incorporated into a general discrete velocity framework, such as
the unified gas-kinetic scheme. Firstly, a global velocity mesh is used to
prevent the interpolation of the VDFs at the physical interface during the
calculation of the microscopic fluxes, maintaining the program's high level of
parallelism. Secondly, rather than utilizing costly interpolation, the VDFs on
a new velocity space were reconstruction using the ``consanguinity"
relationship. In other words, a split child node's VDF is the same as its
parent's VDF, and a merged parent's VDF is the average of its children's VDFs.
Additionally, the discrete deviation of the equilibrium distribution functions
is employed to maintain the proposed method's conservation. Moreover, an
appropriate set of adaptive parameters is established to enhance the automation
of the proposed method. Finally, a number of numerical tests are carried out to
validate the proposed method
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