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Extension of the surface-density Monte Carlo technique to heat transfer in nonconvex regions

About: This article is published in Transactions of the American Nuclear Society.The article was published on 1974-01-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Dynamic Monte Carlo method & Monte Carlo method.
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Journal ArticleDOI
Jovan Zagajac1
TL;DR: A fast method to compute estimates of field values at a few critical points that uses simple and robust geometric tools that is based on an old technique-integrating PDEs through stochastic sampling-that is accelerated through the use of ray representations (ray-reps).
Abstract: Much of the analysis done in engineering design involves the solution of partial differential equations (PDEs) that are subject to initial-value or boundary-value conditions; generically, these are called "field problems". Finite-element and finite-difference methods (FEM, FDM) are the predominant solution techniques, but these are often too expensive or too tedious to use in the early phases of design. What's needed is a fast method to compute estimates of field values at a few critical points that uses simple and robust geometric tools. This paper describes such a method. It is based on an old technique-integrating PDEs through stochastic (Monte Carlo) sampling-that is accelerated through the use of ray representations (ray-reps). In the first (pre-processing) stage, the domain (generally a mechanical part) is coherently sampled to produce a ray-rep. The second stage involves the usual stochastic sampling of the field, which is now enhanced by exploiting the semi-discrete character of ray-reps. The method is relatively insensitive to the complexity of the shape being analyzed, and it has adjustable precision. Its mechanics and advantages are illustrated by using Laplace's equation as an example.

13 citations

Proceedings ArticleDOI
Jovan Zagajac1
01 Dec 1995
TL;DR: A method based on an old technique-integrating PDEs through stochastic (Monte Carlo) sampling-that is accelerated through the use of ray representations that is relatively insensitive to the complexity of the shape being analyzed, and it has adjustable precision.
Abstract: Much of the analysis done in engineering design involves the solution of partial differential equations (PDEs) that are subject to initial-value or boundary-value conditions; generically these are called "field problems." Finite-element and finite-difference methods (FEM, FDM) are the predominant solution techniques, but these are often too expensive or too tedious to use in the early phases of design. What's needed is a fast method to compute estimates of field values at a few critical points that uses simple and robust geometric tools. This paper describes such a method. It is based on an old technique-integrating PDEs through stochastic (Monte Carlo) sampling-that is accelerated through the use of ray representations. In the first (pre-processing) stage, the domain (generally a mechanical part) is coherently sampled to produce a ray-rep. The second stage involves the usual stochastic sampling of the field, which is now enhanced by exploiting the semi-discrete character of ray-reps. The method is relatively insensitive to the complexity of the shape being analyzed, and it has adjustable precision. Its mechanics and advantages are illustrated by using Laplace's equation as an example.

10 citations

Journal ArticleDOI
TL;DR: In this paper, a boundary-dispatch Monte Carlo (Exodus) method is developed, in which the particles are dispatched from the boundaries of a conductive medium or source of heat.
Abstract: A boundary-dispatch Monte Carlo (Exodus) method, in which the particles are dispatched from the boundaries of a conductive medium or source of heat, is developed. A fixed number of particles are dispatched from a boundary node to the nearest internal node. These particles make random walks within the medium similar to that of the conventional Monte Carlo method. Once a particle visits an internal node, a number equal to the temperature of the boundary node from which particles are dispatched is added to a counter. Performing this procedure for all boundary nodes, the temperature of a node can be determined by dividing the flag, or the counter, of this node by the total number of particle visits to this node. Two versions of the boundary-dispatch method (BDM) are presented, multispecies and bispecies BDM. The results of bispecies BDM based on the Exodus dispatching method compare well with the Gauss-Seidel method in both accuracy and computational time. Its computational time is much less than the shrinkin...

9 citations

Proceedings ArticleDOI
17 Jun 1996
TL;DR: In this article, an uncertainty computer model for generic laser/material heating interactions that incorporates probabilistic design (Monte Carlo sampling based) assessment methods was developed, and an analysis of an example problem was performed which involved laser heating of an Al 2024 slab to demonstrate the applicability of the overall uncertainty assessment process.
Abstract: A study has recently been initiated to develop an uncertainty computer model for generic laser/material heating interactions that incorporates probabilistic design (Monte Carlo sampling based) assessment methods. Using this model, an analysis of an example problem was performed which involved laser heating of an Al 2024 slab to demonstrate the applicability of the overall uncertainty assessment process, as well as to provide insight into the usefulness of this design assessment methodology from an engineering viewpoint. This paper summarizes the results of this initial study effort. (Author)

2 citations

Proceedings ArticleDOI
15 Jun 1998
TL;DR: In this article, a study was performed to develop and apply uncertainty computer model for generic laser heating problems that incorporate probabilistic design (Monte Carlo sampling based) assessment methods.
Abstract: For laser irradiation of spacecraft components it is difficult to predict with accuracy the moment (time) and type of failure of. This difficulty is due to the inherent nonlinear nature of the problem, and the uncertainties associated with the irradiation source intensity, interaction cross-section and view angle; the property state of the material(s) being heated; the surface effective emissivity/absorptivity, and the surface radiation view factor(s). The materials physical properties on a spacecraft may also change greatly over time, due to exposure to the space environment. To quantify these uncertainties, a study was performed to develop and apply uncertainty computer model for generic laser heating problems that incorporate probabilistic design (Monte Carlo sampling based) assessment methods. Key parameter uncertainties were characterized and ranked for numerous example problem applications, and the influence of various Monte Carlo sampling approach parameters on the assessment results were also examined. Additionally, a two-dimensional analysis was performed to characterize parameter uncertainties associated with heating of a material that has been exposed to a space environment over a period of time. The influence of specifying various surface boundary conditions, laser beam profiles and coverage area ratios on two-dimensional heating was also investigated. Lastly, the usefulness of the overall uncertainty analysis methodology to * Doctoral Student; Currently Chief

1 citations