A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows IV: full Boltzmann and Model Equations

Fluid dynamic equations are valid in their respective modeling scales. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the flow study in this regime. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well

Particle simulation of micro-scale gas flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77058/1/AIAA-2001-876-485.pd

Theoretical Development of the Information Preservation Method for Strongly Nonequilibrium Gas Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76837/1/AIAA-2005-4828-755.pd

Modeling Gas Nucleation and Condensation Using the Direct Simulation Monte Carlo Method

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77215/1/AIAA-2005-4831-470.pd

Valid Physical Processes from Numerical Discontinuities in Computational Fluid Dynamics

Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting from the discontinuity, a Riemann problem in the Godunov method is solved for the flux evaluation across the cell interface in a finite volume scheme. With the increasing of Mach number in the CFD simulations, the adaptation of the Riemann solver seems introduce intrinsically a mechanism to develop instabilities in strong shock regions. Theoretically, the Riemann solution of the Euler equations are based on the equilibrium assumption, which may not be valid in the non-equilibrium shock layer. In order to clarify the flow physics from a discontinuity, the unsteady flow behavior of one-dimensional contact and shock wave is studied on a time scale of (0~10000) times of the particle collision time. In the study of the non-equilibrium flow behavior from a discontinuity, the collision-less Boltzmann equation is first used for the time scale within one particle collision time, then the direct simulation Monte Carlo (DSMC) method will be adapted to get the further evolution solution. The transition from the free particle transport to the dissipative Navier-Stokes (NS) solutions are obtained as an increasing of time. The exact Riemann solution becomes a limiting solution with infinite number of particle collisions. For the high Mach number flow simulations, the points in the shock transition region, even though the region is enlarged numerically to the mesh size, should be considered as the points inside a highly non-equilibrium shock layer

Rarefied Background Flow in a Vacuum Chamber

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76815/1/AIAA-2005-4660-157.pd

Rarefied Background Flow in a Vacuum Chamber Equipped with One-Sided Pumps

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76471/1/AIAA-19178-970.pd

Development of an information preservation method for subsonic, micro-scale gas flows

The development of an information preservation (IP) method is described in this paper. This effort is aimed at increasing our understanding of rarefied gas behavior of subsonic, micro-scale gas flows. The IP method preserves macroscopic information of the flow in the simulated particles. It applies conservation laws for binary collisions of the particles following the movement in the DSMC method, and updates the information using the Euler equations. The IP results exhibit very low levels of statistical scatter, which helps apply the method to low speed gas flows. A difficulty in implementing the IP method is also discussed. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87370/2/547_1.pd

A Hybrid Continuum / Particle Approach for Micro‐Scale Gas Flows

A hybrid continuum/particle approach is proposed for micro scale gas flows in this paper. The approach couples the DSMC‐IP method and a Navier‐Stokes solver with an adaptive interface. The continuum solver uses the particle cells as ghost cells because the IP method preserves the hydrodynamic information that the continuum solver uses. In order to generate particles from the continuum side, two strategies are proposed. The first one uses a condition similar to the Marshak condition in generating particles through the interface. The second strategy adopts buffer cells and reservoir cells, which avoids directly generating particles. The interface is determined by a continuum breakdown parameter that is evaluated in every time step. In order to track the interface, a mapping technique is used in the code. Numerical examples show that the hybrid approach couples the continuum solver and the particle method very smoothly. Simulated results also show the effects of the cutoff value of the continuum breakdown parameter. © 2003 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87933/2/752_1.pd

Numerical simulation of gas flow over micro-scale airfoils

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76512/1/AIAA-2001-3071-891.pd