Hai P. Le

Complexity reduction of collisional-radiative kinetics for atomic plasma

Thermal non-equilibrium processes in partially ionized plasmas can be most accurately modeled by collisional-radiative kinetics. This level of detail is required for an accurate prediction of the plasma. However, the resultant system of equations can be prohibitively large, making multi-dimensional and unsteady simulations of non-equilibrium radiating plasma particularly challenging. In this paper, we present a scheme for model reduction of the collisional-radiative kinetics, by combining energy levels into groups and deriving the corresponding macroscopic rates for all transitions. Although level-grouping is a standard approach to this type of problem, we provide here a mechanism for achieving higher-order accuracy by accounting for the level distribution within a group. The accuracy and benefits of the scheme are demonstrated for the generic case of atomic hydrogen by comparison with the complete solution of the master rate equations and other methods.

GPU-based flow simulation with detailed chemical kinetics

Abstract The current paper reports on the implementation of a numerical solver on the Graphic Processing Units (GPUs) to model reactive gas mixtures with detailed chemical kinetics. The solver incorporates high-order finite volume methods for solving the fluid dynamical equations coupled with stiff source terms. The chemical kinetics are solved implicitly via an operator-splitting method. We explored different approaches in implementing a fast kinetics solver on the GPU. The detail of the implementation is discussed in the paper. The solver is tested with two high-order shock capturing schemes: MP5 (Suresh and Huynh, 1997) [9] and ADERWENO (Titarev and Toro, 2005) [10] . Considering only the fluid dynamics calculation, the speed-up factors obtained are 30 for the MP5 scheme and 55 for ADERWENO scheme. For the fully-coupled solver, the performance gain depended on the size of the reaction mechanism. Two different examples of chemistry were explored. The first mechanism consisted of 9 species and 38 reactions, resulting in a speed-up factor up to 35. The second, larger mechanism, consisted of 36 species and 308 reactions, resulting in a speed-up factor of up to 40.

Modeling of inelastic collisions in a multifluid plasma: Ionization and recombination

A model for ionization and recombination collisions in a multifluid plasma is formulated using the framework introduced in previous work [H. P. Le and J.-L. Cambier, Phys. Plasmas 22, 093512 (2015)]. The exchange source terms for density, momentum, and energy are detailed for the case of electron induced ionization and three body recombination collisions with isotropic scattering. The principle of detailed balance is enforced at the microscopic level. We describe how to incorporate the standard collisional-radiative model into the multifluid equations using the current formulation. Numerical solutions of the collisional-radiative rate equations for atomic hydrogen are presented to highlight the impact of the multifluid effect on the kinetics.

Modeling of inelastic collisions in a multifluid plasma: Excitation and deexcitation

We describe here a model for inelastic collisions for electronic excitation and deexcitation processes in a general, multifluid plasma. The model is derived from kinetic theory, and applicable to any mixture and mass ratio. The principle of detailed balance is strictly enforced, and the model is consistent with all asymptotic limits. The results are verified with direct Monte Carlo calculations, and various numerical tests are conducted for the case of an electron-hydrogen two-fluid system, using a generic, semi-classical model of collision cross sections. We find that in some cases, the contribution of inelastic collisions to the momentum and thermal resistance coefficients is not negligible, in contrast to the assumptions of current multifluid models. This fundamental model is also applied to ionization and recombination processes, the studies on which are currently underway.

Development of a Flow Solver with Complex Kinetics on the Graphic Processing Units

Abstract : In the current work, we have implemented a numerical solver on the Graphic Processing Units (GPU) to solve the reactive Euler equations with detailed chemical kinetics. The solver incorporates high-order finite volume methods for solving the fluid dynamical equations and an implicit point solver for the chemical kinetics. Generally, the computing time is dominated by the time spent on solving the kinetics which can be benefitted from the computing power of the GPUs. Preliminary investigation shows that the performance of the kinetics solver strongly depends on the mechanism used in the simulations. The speed-up factor obtained in the simulation of an ideal gas ranges from 30 to 55 compared to the CPU. For a 9-species gas mixture, we obtained a speed-up factor of 7.5 to 9.5 compared to the CPU. For such a small mechanism, the achieved speed-up factor is quite promising. This factor is expected to go much higher when the size of the mechanism is increased. The numerical formulation for solving the reactive Euler equations is briefly discussed in this paper along with the GPU implementation strategy. We also discussed some preliminary performance results obtained with the current solver.

Monte Carlo simulation of excitation and ionization collisions with complexity reduction

Abstract Kinetic simulation of plasmas with detailed excitation and ionization collisions presents a significant computational challenge due to the multiscale feature of the collisional rates. In the present work, we propose a complexity reduction method based on atomic level grouping for modeling excitation and ionization collisions. High order of accuracy of the reduction method is realized by allowing an internal distribution within each group. We apply the reduction method to the standard Monte Carlo collision algorithm to model an atomic Hydrogen plasma. Numerical results suggest that the stiffness of the collisional kinetics can be significantly reduced with minimal loss in accuracy.

Coarse-grained Monte Carlo simulation of excitation and ionization collisions

Kinetic simulation of plasmas with detailed excitation and ionization collisions presents a significant computational challenge due to the multiscale feature of the collisional rates. Direct numerical simulation of these collisions using Monte Carlo method requires a large number of samples to resolve all the fast collisional time scales, which is often not necessary and make the simulation very inefficient. In this paper, we present a coarse-graining method to reduce the complexity of detailed excitation and ionization kinetics. The method is then applied to the standard Monte Carlo collision algorithm for simulating a partially ionized Hydrogen plasma. We show that the computational cost can be reduced at minimal loss of accuracy.