Mathematics Department, Michigan State University, D304 Wells Hall, East Lansing, MI 48824-1027, United StatesJournal of Computational Physics (Impact Factor: 2.43). 09/2008; 227(17):8035-8064. DOI: 10.1016/j.jcp.2008.04.038
This work concerns the development of a gridless method for modeling the inter-particle collisions of a gas. Conventional fixed-grid algorithms are susceptible to grid-mismatch to the physical system, resulting in erroneous solutions. On the contrary, a gridless algorithm can be used to simulate various physical systems without the need to perform grid-mesh optimization. An octree algorithm provides the gridless character to a direct simulation Monte Carlo (DSMC) code by automatically sorting nearest-neighbor gas particles into local clusters. Automatic clustering allows abstraction of the DSMC algorithm from the physical system of the problem in question. This abstraction provides flexibility for domains with complex geometries as well as a decreased code development time for a given physical problem. To evaluate the practicality of this code, the time required to perform the gridless overhead from the octree sort is investigated. This investigation shows that the gridless method can indeed be practical and compete with other DSMC codes. To validate gridless DSMC, results of several benchmark simulations are compared to results from a fixed-grid code. The benchmark simulations include several Couette flows of differing Knudsen number, low-velocity flow past a thin plate, and two hypersonic flows past embedded objects at a Mach number of 10. The results of this comparison to traditional DSMC are favorable. This work is intended to become part of a larger gridless simulation tool for collisional plasmas. Corresponding work includes a gridless field solver using an octree for the evaluation of long range electrostatic forces. We plan to merge the two methods creating a gridless framework for simulating collisional-plasmas.
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Conference Paper: Importance Sampling Based Direct Simulation Monte Carlo Method[Show abstract] [Hide abstract]
ABSTRACT: For prediction of nonequilibrium flows, we propose a novel and efficient approach known as importance sampling direct simulation Monte Carlo (ISDSMC) for the solution of the Boltzmann equation. In this particle in cell approach, the computational particles are initially assigned weights (or importance) based on constraints on generalized moments of velocity. The solution of the Boltzmann equation is achieved by use of (i) a streaming operator which streams the computational particles and (ii) a collision operator where the representative collision pairs are selected stochastically based on particle weights. With the scatter reduced, ISDSMC can be applied to a range of problems, especially where the signal-to-noise ratio is small such as in microflows. Performance of ISDSMC approach is evaluated using analysis of three canonical microflows, namely (i) thermal Couette flow, (ii) velocity-slip Couette flow and (iii) Poiseulle flow. Our results indicate good agreement between results obtained from ISDSMC and conventional DSMC methods. Besides leading to a reduction in computational cost, ISDSMC also results in a reduction in statistical scatter compared to conventional direct simulation Monte Carlo (DSMC). The potential applicability of this (ISDSMC) approach to granular flows is also demonstrated using a study of homogeneous relaxation of granular gas and the results based on ISDSMC show good agreement with analytical solution given by Haff’s law.
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ABSTRACT: Parallel code presents a non-trivial problem of load balancing computational workload throughout a system of hardware and software resources. The task of load balancing is further complicated when the number of allowable processors changes through time. This paper presents a two-component load-balancing mechanism using optimal initial workload distribution and dynamic load maintenance. The initial guess is provided by inversion of the workload distribution function. Workload distribution inversion enables efficient domain decomposition for arbitrary workloads and easily compensates for changes in system resources. Dynamic load balancing is provided by process feedback control as used, for example, in control mechanisms of physical processes. Proportional, integral, and differential (PID) feedback readily allows controls to compensate for runtime-changes of the workload distribution function. This paper demonstrates a one-dimensional realization of the ideas presented here. We apply this load-balancing technique to our gridless direct simulation Monte Carlo algorithm. We demonstrate that the method does indeed maintain uniform workload distribution across available resources as the workload and usable system resources undergo change through time.
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ABSTRACT: One main factor governing overall accuracy of Direct Simulation Monte Carlo (DSMC) calculations is the separation between particle pairs during binary collision operations. In many DSMC applications, the dependence of simulation accuracy on collision separation may be quantified through the ratio of the mean collision separation (MCS) in some principle direction to the local mean free path λ. This principle direction is aligned with flowfield gradients, and should, for example, be normal to the surface within boundary layer regions. In this work, a set of new techniques for collision partner selection are proposed in order to efficiently reduce unidirectional MCS/λ relative to existing selection schemes. Accuracy and efficiency of the new techniques are assessed through comparison with several existing techniques, for a representative hypersonic flow over a forward facing step. Particularly favorable qualities are demonstrated for a scheme which involves gradient aligned ordering of particle information arrays through quicksort operations.