Browsing by Author "Cave, H. M."

Now showing 1 - 13 of 13

A true-direction reconstruction of the quiet direct simulation method for inviscid gas flows
(2013-11-01)
Lin, Y. -J.
;
Smith, M. R.
;
Kuo, F. -A.
;
Cave, H. M.
;
Huang, J. -C.
In this paper, a true-direction flux reconstruction of the second-order quiet direct simulation (QDS-2N) Smith et al. (2009)[3] as an equivalent Euler equation solver, called QDS-N-2, is proposed. Because of the true-directional nature of QDS, where volume-to-volume (true-direction) fluxes are computed, as opposed to fluxes at cell interfaces as employed by traditional finite volume schemes, a volumetric reconstruction is required to reach a totally true-direction scheme. The conserved quantities are permitted to vary (according to a polynomial expression) across all simulated dimensions. Prior to the flux computation, QDS particles are introduced using properties based on weighted moments taken over the polynomial reconstruction of the conserved quantity fields. The resulting flux expressions are shown to exactly reproduce the existing second-order extension for a one-dimensional flow, while providing a means for true multi-dimensional reconstruction. The new reconstruction is demonstrated in several verification studies. These include a shock-bubble interaction problem, an Euler-four-shock interaction problem, and the advection of a vortical disturbance. These results are presented, and the increased computation time and the effect of higher-order extension are discussed in this paper. The results show that the proposed multi-dimensional reconstruction provides a significant increase in the accuracy of the solution. We show that, despite the increase in the computational expense, the computational speed of the proposed QDS-N-2 method is several times higher than that of the previously proposed QDS-2N scheme for a fixed degree of numerical accuracy, at least, for the test problem of the advection of vertical disturbances. (C) 2013 Published by Elsevier B.V.
An improved Quiet Direct Simulation method for Eulerian fluids using a second-order scheme
(2009-04-01)
Smith, M. R.
;
Cave, H. M.
;
Wu, J. -S.
;
Jermy, M. C.
;
Chen, Y. -S.
In this paper, a second-order scheme for the Quiet Direct Simulation (QDS) of Eulerian fluids is proposed. The QDS method replaces the random sampling method used in Direct Simulation Monte Carlo (DSMC) methods with a technique whereby particles are moved, have their properties distributed onto a mesh, are destroyed and then are recreated deterministically from the properties stored on the mesh using Gauss-Hermite quadrature weights and abscissas. Particles are permitted to move in physically realistic directions so flux exchange is not limited to cells sharing an adjacent interface as in conventional, direction decoupled finite volume solvers. In this paper the method is extended by calculating the fluxes of mass, momentum and energy between cells assuming a linear variation of density, temperature and velocity in each cell and using these fluxes to update the mass, velocity and internal energy carried by each particle. This Euler solver has several advantages including large dynamic range, no statistical scatter in the results, true direction fluxes to all nearby neighbors and is computationally inexpensive. The second-order method is found to reduce the numerical diffusion of QDS as demonstrated in several verification studies. These include unsteady shock tube flow, a two-dimensional blast wave and of the development of Mach 3 flow over a forward facing step in a wind tunnel, which are compared with previous results from the literature wherever is possible. Finally the implementation of QUIETWAVE, a rapid method of simulating blast events in urban environments, is introduced and the results of a test case are presented. (C) 2008 Elsevier Inc. All rights reserved.
CVD Flow Field Modeling Using the Quiet Direct Simulation (QDS) Method
(2009)
Cave, H. M.
;
Lim, C. -W.
;
Jermy, M. C.
;
Wu, J. -S.
;
Smith, M. R.
In this paper, the Quiet Direct Simulation (QDS) method is used to model the unsteady jet development in a Pulsed Pressure Chemical Vapour Deposition (PP-CVD) reactor. QDS is a novel method of gas flow simulation which is able to compute true-direction fluxes of mass, momentum and energy in a computationally efficient and accurate manner. The scheme is ideal for the simulation of novel CVD processes like PP-CVD which include highly unsteady flow structures and which has previously proved extremely difficult to simulate. Here, the axisymmetric QDS solver is outlined and the injection phase of a PP-CVD reactor is simulated.
DREAM: An Efficient Methodology for DSMC Simulation of Unsteady Processes
(2009)
Cave, H. M.
;
Jermy, M. C.
;
Tseng, K. C.
;
Wu, J. S.
;
機械工程學系
A technique called the DSMC Rapid Ensemble Averaging Method (DREAM) for reducing the statistical scatter in the output from unsteady DSMC simulations is introduced. During post-processing by DREAM, the DSMC algorithm is re-run multiple times over a short period before the temporal point of interest thus building up a combination of time- and ensemble-averaged sampling data. The particle data is regenerated several mean collision times before the output time using the particle data generated during the original DSMC run. This methodology conserves the original phase space data from the DSMC run and so is suitable for reducing the statistical scatter in highly non-equilibrium flows. In this paper, the DREAM-II method is investigated and verified in detail. Propagating shock waves at high Mach numbers (Mach 8 and 12) are simulated using a parallel DSMC code (PDSC) and then post-processed using DREAM. The ability of DREAM to obtain the correct particle velocity distribution in the shock structure is demonstrated and the reduction of statistical scatter in the output macroscopic properties is measured. DREAM is also used to reduce the statistical scatter in the results from the interaction of a Mach 4 shock with a square cavity and for the interaction of a Mach 12 shock on a wedge in a channel.
General Higher Order Extension to the Quiet Direct Simulation Method
(2011)
Lin, Y. -J.
;
Smith, M. R.
;
Cave, H. M.
;
Huang, J. -C.
;
Wu, J. -S.
Presented is the multi-dimensional extension of the Quiet Direct Simulation (QDS) method to general, higher order spatial accuracy. Due to the true directional nature of QDS, where volume-to-volume fluxes are computed as opposed to fluxes at cell interfaces, a volumetric reconstruction is required. In this approach, the conserved quantities are permitted to vary (according to a polynomial expression) across all simulated dimensions. Prior to flux computation, QDS particles are introduced using properties based on weighted moments taken over the polynomial reconstruction of conserved quantity fields. The resulting flux expressions are shown to exactly reproduce existing 2(nd) order extensions (for one-dimensional flows) while providing means for true multi-dimensional reconstruction and general higher order extensions. Here we will show a typical comparison among different spatial order extensions of QDS and other WENO (5(th) order accurate) based numerical scheme. The extension is demonstrated up to 5(th) order spatial accuracy and is shown to be comparable to or more accurate than the other higher order schemes.
Implementation of a transient adaptive sub-cell module for the parallel-DSMC code using unstructured grids
(2010-08-01)
Su, C. C.
;
Tseng, K. C.
;
Cave, H. M.
;
Wu, J. S.
;
Lian, Y. Y.
A method of transient adaptive sub-cells (TAS) suitable for unstructured grids that is modified from the existing one for the structured grids of DSMC is Introduced. The TAS algorithm is implemented within the framework of a parallelized DSMC code (PDSC). Benchmarking tests are conducted for steady driven cavity flow, steady hypersonic flow over a two-dimensional cylinder, steady hypersonic flow over a cylinder/flare and the unsteady vortex shedding behind a two-dimensional cylinder The use of TAS enables a reduction in the computational expense of the simulation since larger sampling cells and less simulation particles can be employed. Furthermore, the collision quality of the simulation is maintained or improved and the preservation of property gradients and vorticity at the scale of the sub-cells enables correct unsteady vortex shedding frequencies to be predicted The use of TAS in a parallel-DSMC code allows simulations of unsteady processes at a level to be carried out efficiently, accurately and with acceptable computational time (C) 2010 Elsevier Ltd All rights reserved
Implementation of the Transient Adaptive Sub-Cell Module for the Parallel DSMC Code
(2009)
Tseng, K. C.
;
Cave, H. M.
;
Kuo, T. C.
;
Jermy, M. C.
;
Krumdieck, S. P.
A method of transient adaptive sub-cells (TAS) suitable for unstructured grids in Direct Simulation Monte Carlo (DSMC) simulations is introduced. The TAS algorithm is implemented within the frame work of a parallelized DSMC code (PDSC). Benchmarking tests are conducted for driven cavity (low, hypersonic flow over a two-dimensional cylinder and the unsteady vortex shedding behind a two-dimensional cylinder. The use of TAS enabled a reduction in the computational expense of the simulation since larger sampling cells and less simulation particles could be employed. Furthermore, the collision quality of the simulation was maintained or improved and the preservation of property gradients and vorticity at the scale of the sub-cells enabled correct unsteady vortex shedding frequencies to be predicted. The use of TAS in a parallel DSMC code allows simulations of unsteady processes at a near continuum level to be carried out efficiently, accurately and with acceptable computational times.
Implementation of unsteady sampling procedures for the parallel direct simulation Monte Carlo method
(2008-06-01)
Cave, H. M.
;
Tseng, K. -C.
;
Wu, J. -S.
;
Jermy, M. C.
;
Huang, J. -C.
An unsteady sampling routine for a general parallel direct simulation Monte Carlo method called PDSC is introduced, allowing the simulation of time-dependent flow problems in the near continuum range. A post-processing procedure called DSMC rapid ensemble averaging method (DREAM) is developed to improve the statistical scatter in the results while minimising both memory and simulation time. This method builds an ensemble average of repeated runs over small number of sampling intervals prior to the sampling point of interest by restarting the flow using either a Maxwellian distribution based on macroscopic properties for near equilibrium flows (DREAM-I) or output instantaneous particle data obtained by the original unsteady sampling of PDSC for strongly non-equilibrium flows (DREAM-II). The method is validated by simulating shock tube flow and the development of simple Couette flow. Unsteady PDSC is found to accurately predict the flow field in both cases with significantly reduced run-times over single processor code and DREAM greatly reduces the statistical scatter in the results while maintaining accurate particle velocity distributions. Simulations are then conducted of two applications involving the interaction of shocks over wedges. The results of these simulations are compared to experimental data and simulations from the literature where there these are available. In general, it was found that 10 ensembled runs of DREAM processing could reduce the statistical uncertainty in the raw PDSC data by 2.5-3.3 times, based on the limited number of cases in the present study. (c) 2008 Published by Elsevier Inc.
Multi-Species Fluxes for the Parallel Quiet Direct Simulation (QDS) Method
(2011-01-01)
Cave, H. M.
;
Lim, C. -W.
;
Jermy, M. C.
;
Krumdieck, S. P.
;
Smith, M. R.
Fluxes of multiple species are implemented in the Quiet Direct Simulation (QDS) scheme for gas flows. Each molecular species streams independently. All species are brought to local equilibrium at the end of each time step. The multi species scheme is compared to DSMC simulation, on a test case of a Mach 20 flow of a xenon/helium mixture over a forward facing step. Depletion of the heavier species in the bow shock and the near-wall layer are seen. The multi-species QDS code is then used to model the flow in a pulsed-pressure chemical vapour deposition reactor set up for carbon film deposition. The injected gas is a mixture of methane and hydrogen. The temporal development of the spatial distribution of methane over the substrate is tracked.
Quiet Direct Simulation (QDS) of Viscous Flow Using the Chapman-Enskog Distribution
(2011-01-01)
Smith, M. R.
;
Kuo, F. -A.
;
Cave, H. M.
;
Jermy, M. C.
;
Wu, J. -S.
Presented here is the QDS method modified to employ an arbitrary governing velocity probability distribution. An algorithm is presented for the computation of QDS particle "blueprints". The method, which employs a known continuous velocity probability distribution function, uses a set of fixed QDS particle "weights", which can be arbitrarily selected. Provided the weights, particle "blueprint" velocities are computed by taking multiple moments around the governing velocity probability distribution function to provide the discrete representation employed by QDS. In particular, we focus on the results obtained when the governing distribution function is the Chapman-Enskog distribution function. Results are shown for several benchmark tests including a one dimensional standing shock wave and a two dimensional lid driven cavity problem. Finally, the performance of QDS when applied to General Purpose computing on Graphics Processing Units (GPGPU) is demonstrated.
The direction decoupled Quiet Direct Simulation method for rapid simulation of axisymmetric inviscid unsteady flow in pulsed pressure chemical vapour deposition
(2013-11-05)
Lim, C. W.
;
Smith, M. R.
;
Cave, H. M.
;
Jermy, M. C.
;
Wu, J. -S.
Pulsed Pressure-Chemical Vapour Deposition (PP-CVD) is a thin film deposition process which employs a highly unsteady flow with wide dynamic range of pressure. The large, time-varying density gradient during a PP-CVD process cycle produces a flow field in which the Knudsen number varies from the near-continuum to the rarefied regimes, making Direct Simulation Monte Carlo (DSMC) prohibitively expensive. The present directional decoupled Quiet Direct Simulation (DD-QDS) method is a novel kinetic-based flux scheme that computes fluxes of mass, momentum and energy at the interface of computational cells in a highly computationally efficient manner. The Maxwell-Boltzmann equilibrium distribution is enforced locally at each computational cell at each time step. In this paper, an axisymmetric second order directional decoupled QDS scheme is used to simulate highly unsteady flows encountered in PP-CVD reactor. Two simulations were conducted to investigate the PP-CVD reactor flow field at 1 Pa and 1 kPa reactor base pressures. The assumption of the local Maxwell-Boltzmann equilibrium distribution used in the QDS scheme is verified by examining the gradient length local Knudsen number based on the density, and by estimating the average number of molecular collisions within each computational cell in one computational time step. The validity of the local equilibrium assumption is found satisfactory at 1 kPa reactor based pressure but not at 1 Pa. The limitation of the QDS scheme in modelling PP-CVD flow was also investigated. The time required to establish the quasi-steady under-expanded jet is found to be similar to 4 ms, and the jet dissipates within 0.5 ms of the end of injection. This important information is required to set up PP-CVD operating conditions which give uniform film deposition. (C) 2013 Elsevier Ltd. All rights reserved.
Two-level virtual mesh refinement algorithm in a parallelized DSMC Code using unstructured grids
(2011-09-01)
Su, C. C.
;
Tseng, K. C.
;
Wu, J. S.
;
Cave, H. M.
;
Jermy, M. C.
In this paper, a virtual mesh refinement (VMR) algorithm for unstructured grids is developed and verified in the parallelized direct simulation Monte Carlo code (PDSC). This algorithm is a two-level virtual mesh refinement, in which the background mesh is refined based on an initial DSMC simulation. The refined cells are arranged in a way similar to the structured grid, which makes the particle tracing on them very efficient, unlike unstructured grids. These virtual cells are used for particle collision and sampling. Only those refined cells which contain the centroid of background cells are used for outputting macroscopic data. Two hypersonic flows with purely quadrilateral and mixed triangular-quadrilateral mesh were used to verify this new mesh-refining algorithm. Results show that the case using VMR can faithfully reproduce the benchmark case with a much reduced computational time. (C) 2011 Elsevier Ltd. All rights reserved.
Validity and Inherent Viscosity of the Quiet Direct Simulation Method
(2011-01-01)
Jermy, M. C.
;
Lim, C. -W.
;
Cave, H. M.
;
機械工程學系
;
Department of Mechanical Engineering
The Quiet Direct Simulation (QDS) scheme is a numerical method for modelling gas flows, based on kinetic theory, with some similarities to the Lattice Boltzmann Method (LBM). It differs from LBM notably in that the discrete molecular velocities are not constant but are reset each timestep according to local values of bulk velocity and temperature. For this reason it performs well in highly compressible flows. Two features of the scheme limit its accuracy in low Mach number flows. QDS assumes a Maxwell distribution of molecular velocities. The validity of this assumption may be tested by calculating the gradient Knudsen number and average number of collisions per timestep. The separation of collision and streaming leads to excessive diffusion of momentum, leading to a very high effective viscosity of the modelled gas when the grid spacing is larger than the mean free path. This numerical dissipation is different in character from the dissipation due to the finite order of the spatial reconstruction, common to all finite volume methods, which is also present. The effective viscosity is quantified for simple shear flows and tested in models of a 2D channel flow. A crude model of intermolecular collision during streaming is implemented and shown to reduce the effective viscosity.