Reduction of Computing Time and Improvement of Convergence Stability of the Monte Carlo Method Applied to Radiative Heat Transfer With Variable Properties

1989 ◽  
Vol 111 (1) ◽  
pp. 135-140 ◽  
Author(s):  
M. Kobiyama
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Computing Time ◽  
Energy Difference ◽  
Radiative Properties ◽  
Radiative Energy ◽  
Control Element ◽  
The Monte Carlo Method ◽  
The Difference ◽  
Convergence Stability

A modified Monte Carlo method is suggested to reduce the computing time and improve the convergence stability of iterative calculations without losing other excellent features of the conventional Monte Carlo method. In this method, two kinds of radiative bundle are used: energy correcting bundles and property correcting bundles. The energy correcting bundles are used for correcting the radiative energy difference between two successive iterative cycles, and the property correcting bundles are used for correcting the radiative properties. The number of radiative energy bundles emitted from each control element is proportional to the difference in emissive energy between two successive iterative cycles.

scholarly journals Analysis of the Accuracy of the Calculation of the Diaphragm Area by the Monte Carlo Method

2020 ◽  
pp. 22-26
Author(s):  
O. D. Kupko
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Circular Aperture ◽  
The Monte Carlo Method ◽  
Relative Standard ◽  
Uniform Probability Distribution ◽  
Standard Deviations ◽  
The Difference

The process of measuring the area of a circular diaphragm using a device that determines the coordinates of the boundary of the diaphragm is theoretically considered. The Monte Carlo method with a small number of implementations was used. The procedure for calculating the area is described in detail. We considered a circular aperture with a precisely known radius. On the circumference of the diaphragm, the coordinate measuring points vibrated through 0.1, 0.3, 0.6, and π/2 radians vibrated. To simulate random deviations (uncertainties) when measuring coordinates, random additives were used with a uniform probability distribution and a given standard deviation. For each case, the areas were calculated in accordance with the proposed procedure. The difference in the results of calculating the area from the true area depending on the number of measurement points and the standard deviation of random additives is analyzed. It is shown that the ratio of the relative standard deviations of the area to the relative standard deviations of the coordinates is approximately the same for each number of measurements. The dependence of this relationship on the number of measurements is determined. The results obtained are analyzed.

The Past and Future of the Monte Carlo Method in Thermal Radiation Transfer

2021 ◽  
Author(s):  
John R. Howell ◽  
Kyle Daun
Keyword(s):  
Monte Carlo ◽  
Energy Transfer ◽  
Monte Carlo Method ◽  
Radiation Transfer ◽  
Massively Parallel ◽  
Radiative Energy ◽  
Quantum Computers ◽  
The Past ◽  
Radiative Energy Transfer ◽  
The Monte Carlo Method

Abstract The history and progress in Monte Carlo methods applied to radiative energy transfer are reviewed, with emphasis on advances over the past 25 years. Unresolved issues are outlined, and comments are included about the outlook for the method as impacted by the advances in massively parallel and quantum computers.

Evaluation of Free Energy Differences Between Crystalline Phases Using the Lattice-Switch Monte Carlo Method

1997 ◽  
Vol 499 ◽  
Author(s):  
G. J. Ackland ◽  
N. B. Wilding ◽  
A. D. Bruce
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Method ◽  
Hard Spheres ◽  
Energy Difference ◽  
New Method ◽  
Free Energies ◽  
Free Energy Difference ◽  
Crystal Phases ◽  
The Difference

ABSTRACTA new method [1] of calculating the free energy difference between two crystalline structures is presented. The method involves a single simulation which repeatedly transforms the system between the two crystal phases. Since the configurations of both structures are sampled within a single Monte Carlo process, the difference between their free energies can be evaluated directly from the ratio of the measured probabilities of each. Compared with traditional techniques, the method is most advantageous when applied to highly anharmonic systems. To illustrate the method, an application to the free energy difference between the fee and hep structures of hard spheres is described.

scholarly journals Calculations of Alloy Phases with a Direct Monte-Carlo Method

1992 ◽  
Vol 291 ◽  
Author(s):  
J. S. Faulkner ◽  
Yang Wang ◽  
Eva A. Horvath ◽  
G. M. Stocks
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Solid Phase ◽  
Energy Difference ◽  
Cluster Method ◽  
Interatomic Potentials ◽  
The Monte Carlo Method ◽  
Interchange Energy ◽  
Copper Nickel Alloy ◽  
Miscibility Gaps

ABSTRACTA method for calculating the boundaries that describe solid-solid phase transformations in the phase diagrams of alloys is described. The method is first-principles in the sense that the only input is the atomic numbers of the constituents. It proceeds from the observation that the crux of the Monte-Carlo method for obtaining the equilibrium distribution of atoms in an alloy is a calculation of the energy required to replace an A atom on site i with a B atom when the configuration of the atoms on the neighboring sites, κ is specified, δHκ(A→B) = EB(κ)−EA(κ).Normally, this energy difference is obtained by introducing interatomic potentials, vij ,into an Ising Hamiltonian, but we calculate it using the embedded cluster method (ECM). In the ECM an A or B atom is placed at the center of a cluster of atoms with the specified configuration κ ,and the atoms on all the other sites in the alloy are simulated by the effective scattering matrix obtained from the coherent potential approximation. The interchange energy is calculated directly from the electronic structure of the cluster. The table of δHκ(A→B)'s for all configurations κ and several alloy concentrations is used in a Monte Carlo calculation that predicts the phase of the alloy at any temperature and concentration. The detailed shape of the miscibility gaps in the palladium-rhodium and copper-nickel alloy systems are shown.

Study of Light Scattering by TiO2, Ag, and SiO2 Nanofluids with Particle Diameters of 20-60 nm

2019 ◽  
Vol 60 ◽  
pp. 1-20 ◽  
Author(s):  
Jasman Y.H. Chai ◽  
Basil T. Wong
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Volume Fraction ◽  
Radiative Transfer Equation ◽  
Mie Theory ◽  
Radiative Properties ◽  
Scattering Coefficients ◽  
The Monte Carlo Method ◽  
Fraction Increase ◽  
Nanoparticle Sizes

In this research, we detailed how the following factors affect the scattering of light by nanofluids: (1) nanoparticle sizes, (2) volume fraction of nanoparticles, and (3) nanoparticle materials. Mie theory was used to calculate the radiative properties of the nanofluids. The radiative properties were then applied into the Radiative Transfer Equation (RTE) to solve for the transmittance and reflectance of light through the nanofluids. The RTE was solved using the Monte Carlo method. Results showed that when the size of nanoparticles and the volume fraction increase, absorption and scattering coefficients increase as well. For silver nanofluids, absorption and scattering coefficients decrease beyond nanoparticle size of about 50 nm. Transmittance of light decreased when nanoparticle sizes increased. When comparing between TiO2, Ag, and SiO2 nanofluids, Ag nanofluids exhibit the highest light absorption followed by TiO2 and SiO2.

To Simulate the Flow Field of Jet Pumps of Plane Model by Using Monte Carlo Method

2011 ◽  
Vol 295-297 ◽  
pp. 1829-1833
Author(s):  
Tong Zhuo Li ◽  
Peng Fei Bi ◽  
Nan Jiang
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Monte Carlo Method ◽  
Flow Field ◽  
Computing Time ◽  
Momentum Equation ◽  
Plane Model ◽  
Fluid Field ◽  
The Monte Carlo Method ◽  
Jet Pumps

First numeric computation of fluid field inside jet pump is conducted with continuity equation and momentum equation of steady fluid under right-angled two-dimension coordinates, and the random walk model is given. As for the method of integrating coupling pressure and momentum equation is adopted. The result is conforming to the flow of reality. Furthermore, the relation of random walk times and computing time and computing errors is analyzed in-depth. The relation of iterative times and computing errors is analyzed. It establishes a foundation for studying the flow field of jet pumps to use the Monte Carlo Method. At the meantime it develops a new field.

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