Jong-Shinn Wu

Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme

Application of variable time-step and unstructured adaptive mesh refinement in parallel three-dimensional Direct Simulation Monte Carlo (DSMC) method is presented. A variable time-step method using the particle fluxes conservation (mass, momentum and energy) across the cell interface is implemented to reduce the number of simulated particles and the number of iterations of transient period towards steady state, without sacrificing the solution accuracy. In addition, a three-dimensional h-refined unstructured adaptive mesh with simple but effective mesh-quality control, obtained from a preliminary parallel DSMC simulation, is used to increase the accuracy of the DSMC solution. Completed code is then applied to compute several external and internal flows, and compared with previous results wherever available.

Large-scale simulations on multiple Graphics Processing Units (GPUs) for the direct simulation Monte Carlo method

In this study, the application of the two-dimensional direct simulation Monte Carlo (DSMC) method using an MPI-CUDA parallelization paradigm on Graphics Processing Units (GPUs) clusters is presented. An all-device (i.e. GPU) computational approach is adopted where the entire computation is performed on the GPU device, leaving the CPU idle during all stages of the computation, including particle moving, indexing, particle collisions and state sampling. Communication between the GPU and host is only performed to enable multiple-GPU computation. Results show that the computational expense can be reduced by 15 and 185 times when using a single GPU and 16 GPUs respectively when compared to a single core of an Intel Xeon X5670 CPU. The demonstrated parallel efficiency is 75% when using 16 GPUs as compared to a single GPU for simulations using 30 million simulated particles. Finally, several very large-scale simulations in the near-continuum regime are employed to demonstrate the excellent capability of the current parallel DSMC method.

An improved Quiet Direct Simulation method for Eulerian fluids using a second-order scheme

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.

Development of a parallel semi-implicit two-dimensional plasma fluid modeling code using finite-volume method

Abstract In this paper, the development of a two-dimensional plasma fluid modeling code using the cell-centered finite-volume method and its parallel implementation on distributed memory machines is reported. Simulated discharge currents agree very well with the measured data in a planar dielectric barrier discharge (DBD). Parallel performance of simulating helium DBD solved by the different degrees of overlapping of additive Schwarz method (ASM) preconditioned generalized minimal residual method (GMRES) for different modeling equations is investigated for a small and a large test problem, respectively, employing up to 128 processors. For the large test problem, almost linear speedup can be obtained by using up to 128 processors. Finally, a large-scale realistic two-dimensional DBD problem is employed to demonstrate the capability of the developed fluid modeling code for simulating the low-temperature plasma with complex chemical reactions.

Development of a Parallel Hybrid Method for the DSMC and NS Solver

A parallel 3-D hybrid DSMC-NS method using the unstructured grid topology has been proposed and developed such that near continuum flows or a region consisting of continuum, slip, and free-molecular flows can be simulated efficiently. A continuum breakdown parameter proposed by Wang and Boyd is used in the present work for determining the choice of solver in spatial domain. A hypersonic flow over a 2-D wedge and other test cases are employed to evaluate and validate the present hybrid method. Preliminary results show the simulation data of the present hybrid method is in good agreement with those of the pure DSMC method. In general, computational time using the hybrid method is lower than that using the pure DSMC method. In addition, the region with strong thermal non-equilibrium cannot be precisely identified by the continuum break down parameter proposed by Wang and Boyd. Future study is needed to develop an appropriate method to identify the thermal non-equilibrium region.

Implementation of unsteady sampling procedures for the parallel direct simulation Monte Carlo method

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.

Parallel adaptive mesh-refining scheme on a three-dimensional unstructured tetrahedral mesh and its applications

The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N 1.5 for Nproc 32. Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson–Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.

Development of a parallel Poisson's equation solver with adaptive mesh refinement and its application in field emission prediction

A parallel electrostatic Poissons equation solver coupled with parallel adaptive mesh refinement (PAMR) is developed in this paper. The three-dimensional Poissons equation is discretized using the Galerkin finite element method using a tetrahedral mesh. The resulting matrix equation is then solved through the parallel conjugate gradient method using the non-overlapping subdomain-by-subdomain scheme. A PAMR module is coupled with this parallel Poissons equation solver to adaptively refine the mesh where the variation of potentials is large. The parallel performance of the parallel Poissons equation is studied by simulating the potential distribution of a CNT-based triode-type field emitter. Results with ∼100 000 nodes show that a parallel efficiency of 84.2% is achieved in 32 processors of a PC-cluster system. The field emission properties of a single CNT triode- and tetrode-type field emitter in a periodic cell are computed to demonstrate their potential application in field emission prediction.

Fluid Modeling of a Nitrogen Atmospheric-Pressure Planar Dielectric Barrier Discharge Driven by a Realistic Distorted Sinusoidal Alternating Current Power Source

One-dimensional self-consistent simulations of a parallel-plate atmospheric-pressure nitrogen dielectric barrier discharge (DBD) are presented. The DBD was driven by a realistic distorted-sinusoidal voltage power source with a frequency of 60 kHz. The simulated discharge currents are in quantitative agreement with experimental measurements. N4+ ions gain more of the input electric power than electrons, which is unlike most glow discharges. The densities of all charged and neutral species increase exponentially with increasing applied peak voltage in the range of 6.2–8.6 kV. The higher the permittivity of the dielectric material, the larger the discharge current and the longer the period of gas breakdown. In addition, the quantity of accumulated charges at each electrode increases with increasing permittivity of the dielectric material. Finally, the increase in dielectric thickness from 1.0 to 2.0 mm greatly reduces the densities of all species and also the plasma absorbed by the power.

Development of a parallel implicit solver of fluid modeling equations for gas discharges

A parallel fully implicit PETSc-based fluid modeling equations solver for simulating gas discharges is developed. Fluid modeling equations include: the neutral species continuity equation, the charged species continuity equation with drift-diffusion approximation for mass fluxes, the electron energy density equation, and Poisson’s equation for electrostatic potential. Except for Poisson’s equation, all model equations are discretized by the fully implicit backward Euler method as a time integrator, and finite differences with the Scharfetter–Gummel scheme for mass fluxes on the spatial domain. At each time step, the resulting large sparse algebraic nonlinear system is solved by the Newton–Krylov–Schwarz algorithm. A 2D-GEC RF discharge is used as a benchmark to validate our solver by comparing the numerical results with both the published experimental data and the theoretical prediction. The parallel performance of the solver is investigated.