Particle-based Monte Carlo Method Research Articles

An efficient asymptotic preserving Monte Carlo method for radiative transfer equations

In this work, an efficient asymptotic preserving Monte Carlo method is developed for nonlinear thermal radiative transfer equations. We derive a new approximate macroscopic equation for the radiation energy density, from an integral solution of the radiation intensity along characteristics of the microscopic equation. We will solve a coupled macro-micro system with a hybrid numerical method. The macroscopic radiation and material energy densities are updated first by using a deterministic finite volume method. The microscopic equation, with the emission source provided from the macroscopic variables, can then be efficiently solved using a particle-based Monte Carlo method. This new approach is uniformly stable, with large time steps independent of scaling parameters and the speed of light. Besides, it can be shown that the method is asymptotic preserving in the diffusive limit for an optically thick regime. Numerical experiments are performed to demonstrate the high efficiency and good performances of our proposed method.

Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by the evolution of macroscopic variables, and guarantees the conservation of the scheme in the final wave-particle formulation. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced. Multiscale preserving means UGKWP method preserves the flow regime from collisionless regime to hydrodynamic regime without requiring the cell size and time step to be less than the mean free path and collision time. Multi-efficiency preserving means the computational cost of the scheme including the computational time and memory cost is on the same level as the most efficient method in the corresponding regime, such as the particle methods in the rarefied regime and hydrodynamic solvers in continuum regime. The UGKWP method is shown to satisfy the MMP requirement. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the discrete ordinate methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include the hypersonic flow passing a circular cylinder at Mach numbers 20 and 30 and Knudsen numbers 1 and 10−4, low speed lid-driven cavity flow, laminar boundary layer, shock structure, and shock tube problems. These results validate the accuracy, efficiency, and multiscale and multi-efficiency property of UGKWP method.

Turbulent piloted partially-premixed flames with varying levels of O2/N2: stability limits and PDF calculations

This paper reports measured stability limits and PDF calculations of piloted, turbulent flames of compressed natural gas (CNG) partially-premixed with either pure oxygen, or with varying levels of O2/N2. Stability limits are presented for flames of CNG fuel premixed with up to 20% oxygen as well as CNG–O2–N2 fuel where the O2 content is varied from 8 to 22% by volume. Calculations are presented for (i) Sydney flame B [Masri et al. 1988] which uses pure CNG as well as flames B15 to B25 where the CNG is partially-premixed with 15–25% oxygen by volume, respectively and (ii) Sandia methane–air (1:3 by volume) flame E [Barlow et al. 2005] as well as new flames E15 and E25 that are partially-premixed with ‘reconstituted air’ where the O2 content in nitrogen is 15 and 25% by volume, respectively. The calculations solve a transported PDF of composition using a particle-based Monte Carlo method and employ the EMST mixing model as well as detailed chemical kinetics. The addition of oxygen to the fuel increases stability, shortens the flames, broadens the reaction zone, and shifts the stoichiometric mixture fraction towards the inner side of the jet. It is found that for pure CNG flames where the reaction zone is narrow (∼0.1 in mixture fraction space), the PDF calculations fail to reproduce the correct level of local extinction on approach to blow-off. A broadening in the reaction zone up to about 0.25 in mixture fraction space is needed for the PDF/EMST approach to be able to capture these finite-rate chemistry effects. It is also found that for the same level of partial premixing, increasing the O2/N2 ratio increases the maximum levels of CO and NO but shifts the peak to richer mixture fractions. Over the range of oxygenation investigated here, stability limits have shown to improve almost linearly with increasing oxygen levels in the fuel and with increasing the contribution of release rate from the pilot.

Three-dimensional deposition topography simulation based on new combinations of flux distribution and surface representation algorithms

The development of a full three-dimensional (3-D) deposition topography simulator is indispensable to the precise estimation of thin film deposition topography on asymmetric deposition geometries. In this study, we expand the application range of the equi-volume rate model (EVRM), a cell-based surface representation algorithm for full 3-D topography simulation, into rigorous flux distribution algorithms such as the Monte Carlo method (MCM) and the ballistic transport and reaction model (BTRM). A new full 3-D deposition topography simulation is conducted based on the new combinations of flux distribution and surface representation algorithms. To ensure the effectiveness of our simulation, we conduct numerous simulations for various deposition geometries with varying sticking coefficients and directionality factors. We also compare the simulation results of MCM-EVRM and BTRM-EVRM versions. From the viewpoint of precise simulated topography, a particle-based MCM has better suitability to a cell-based EVRM than a flux-based BTRM. In addition, from the viewpoint of computational time, the MCM-EVRM method is apt for the complex geometries and for the deposition processes of high sticking coefficient; such as physical vapor deposition and plasma enhanced chemical vapor deposition. In the other hand, the BTRM-EVRM method is suitable for the simple geometries and for the processes of low sticking coefficient such as chemical vapor deposition.