Chieh-Tsan Hung

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 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.

Development of an improved spatial reconstruction technique for the HLL method and its applications

The integral form of the conventional HLL fluxes are presented by taking integrals around the control volume centred on each cell interface. These integrals are demonstrated to reduce to the conventional HLL flux through simplification by assuming spatially constant conserved properties. The integral flux expressions are then modified by permitting the analytical inclusion of spatially linearly varying conserved quantities. The newly obtained fluxes (which are named HLLG fluxes for clarification, where G stands for gradient inclusion) demonstrate that conventional reconstructions at cell interfaces are invalid and can produce unstable results when applied to conventional HLL schemes. The HLLG method is then applied to the solution of the Euler Equations and Shallow Water Equations for various common benchmark problems and finally applied to a 1D fluid modeling for an argon RF discharge at low pressure. Results show that the correct inclusion of flow gradients is shown to demonstrate superior transient behavior when compared to the existing HLL solver and conventional spatial reconstruction without significantly increasing computational expense.

A new paradigm for solving plasma fluid modeling equations

A new paradigm for solving plasma fluid modeling equations is proposed and verified in this paper. Model equations include continuity equations for charged species with drift-diffusion approximation, electron energy equation, and Poisson’s equation. Resulting discretized equations are solved jointly by the Newton–Krylov–Schwarz (NKS) [1] scheme by means of a parallelized toolkit called PETSc. All model equations are nondimensionalized and are discretized using fully implicit finite-difference method with the Scharfetter–Gummel scheme for the fluxes. At electrodes, thermal flux is considered for electrons, while both thermal and drift fluxes are considered for ions. A quasi-1D argon gas discharge with a radio frequency power source (13.56 MHz, Vp−p = 200 Volts), gap distance = 20 mm and 20 mm × 20 mm (100 × 100 mesh points) in size is used as the test case. Results of evolution of potential and plasma number density are shown Fig. 1, which are comparable to previous studies. Table 1 lists all the resulting timings of the present parallelized code using different combination of preconditioners (Additive

A parallel hybrid numerical algorithm for simulating gas flow and gas discharge of an atmospheric-pressure plasma jet

Abstract Development of a hybrid numerical algorithm which couples weakly with the gas flow model (GFM) and the plasma fluid model (PFM) for simulating an atmospheric-pressure plasma jet (APPJ) and its acceleration by two approaches is presented. The weak coupling between gas flow and discharge is introduced by transferring between the results obtained from the steady-state solution of the GFM and cycle-averaged solution of the PFM respectively. Approaches of reducing the overall runtime include parallel computing of the GFM and the PFM solvers, and employing a temporal multi-scale method (TMSM) for PFM. Parallel computing of both solvers is realized using the domain decomposition method with the message passing interface (MPI) on distributed-memory machines. The TMSM considers only chemical reactions by ignoring the transport terms when integrating temporally the continuity equations of heavy species at each time step, and then the transport terms are restored only at an interval of time marching steps. The total reduction of runtime is 47% by applying the TMSM to the APPJ example presented in this study. Application of the proposed hybrid algorithm is demonstrated by simulating a parallel-plate helium APPJ impinging onto a substrate, which the cycle-averaged properties of the 200th cycle are presented. The distribution patterns of species densities are strongly correlated by the background gas flow pattern, which shows that consideration of gas flow in APPJ simulations is critical.

One-dimensional simulation of nitrogen dielectric barrier discharge driven by a quasi-pulsed power source and its comparison with experiments

Parallel-plate nitrogen dielectric barrier discharge (DBD) driven by a quasi-pulsed power source (60 kHz) is simulated using a fully-implicit 1D self-consistent fluid modeling code. Simulated discharged currents of gap distances (0.5, 0.7 and 1.0 mm) agree very well with measured data; while simulated discharged currents of wider gap distance (1.2 mm) fail to reproduce the measured data. It is found that the discharge mode is homogeneous Townsend-like for the former case; while it is filamentary-like for the latter case based on the experimental observation. These findings demonstrate that previous numerical studies showing mode transition by changing the gap distance may require further investigation.

Effect of plasma chemistry on the simulation of helium atmospheric-pressure plasmas

Article history: The effect on the selection of different plasma chemistries for simulating a typical dielectric barrier discharge (DBD) driven by quasi-pulsed power source (20 kHz) is investigated. The numerical simulation was performed by using the one-dimensional self-consistent fluid modeling solver. Our simulation result indicates that the computed temporal current density can be significantly improved by using a complex version of plasma chemistry module rather than the simple one and demonstrates an excellent agreement with the experimental data. The result suggests the metastable, excited and ionic helium related reaction channels, which are important in simulating a DBD, should be taken into account. Furthermore, it also reveals that the power absorption of ions is considerably higher than that of the electron.

On the performance improvement of a parallel 3-D PIC-FEM code

Summary form only given. In the previous ICOPS meeting, we have presented a parallel 3-D PIC code using the finite-element method with an unstructured tetrahedral mesh for the flexibility of modeling objects with complex geometry. In addition, the dynamic domain decomposition using the graph-partitioning technique is employed for a better load balancing among the processors. Parallel efficiency of this code, implemented on HP clusters could be as high as 82% with 32 processors (40 particles per cell, ~30,000 nodes). However, one of the major drawbacks of this code is the relatively poor runtime performance as compared to the previous PIC codes using the finite-difference method with a structured mesh. In this paper, we will present some improvements, including the Poissons equation solver and the particle tracing technique, to greatly enhance the code performance. First, we have replaced the original parallel conjugate gradient method by either a sparse direct matrix solver (MUMPS) for fewer processors ( 10). With the MUMPS for fewer processors, the assembled coefficient matrix is factorized into the L and U matrices once initially and they are stored for further use at each time step. At each time, only the source term (charge density) changes while the L and U matrices remain unchanged, which makes solving the matrix equation very fast. Second, a tetrahedral mesh is replaced by a multi-block hybrid structured-unstructured mesh to both maintain the flexibility of dealing with complicated geometry and the maximal efficiency of particle tracing. In the structured-mesh block with the pure hexahedral cells, the particle tracing takes advantage of the simple relation between mesh coordinate and mesh index, which is very fast. While in the unstructured-mesh block with the mixed tetrahedral and pyramid cells, the similar technique is adopted. A RF capacitive discharge between two circular electrodes in a hexahedral metal chamber is used to demonstrate the performance improvement and preliminary results show reduction of the runtime up to five times can be achieved in the test example