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ABSTRACT
A bidirectionally weighted Monte Carlo method has been developed for radiation transfer in participating media. For every two elementary cells, the radiation exchange is expressed as the weighted combination of those obtained from the forward and reverse Monte Carlo methods. And the weight is derived, so that the standard deviation of the radiation exchange is minimized, in contrast to the forward and reverse methods for the same computing cost. Moreover, this method can be applied to complex systems such as that containing highly spectral media. In benchmark solutions, the method was validated and results in less statistical errors than other types of Monte Carlo methods.
Nomenclature
| f | = | spectral radiation exchange factor of cells |
| G | = | spectral radiation absorption (W) |
| I | = | spectral emissive intensity (W Sr−1 m−3) |
| N | = | number of cells |
| P | = | spectral radiation exchange (W) |
| S | = | area of surface cells (m2) |
| V | = | volume of volumetric cells (m3) |
| = | stochastic estimation | |
| σ | = | standard deviation |
| χ | = | interpolation weight in BWM |
| Greek symbols | = | |
| δ | = | spectral scattering coefficient (m−1) |
| ϵ | = | spectral absorptivity |
| κ | = | spectral absorption coefficient (m−1) |
| Superscripts | = | |
| A, E, O | = | ARM, ERM and ORM |
| B | = | BWM |
| F, R | = | FM and RM |
| S | = | quantity of surface cells |
| 0 | = | black body |
| V | = | quantity of volumetric cells |
| Subscripts | = | |
| i, j | = | elementary cell number |
| ν | = | spectral location (cm−1) |
Nomenclature
| f | = | spectral radiation exchange factor of cells |
| G | = | spectral radiation absorption (W) |
| I | = | spectral emissive intensity (W Sr−1 m−3) |
| N | = | number of cells |
| P | = | spectral radiation exchange (W) |
| S | = | area of surface cells (m2) |
| V | = | volume of volumetric cells (m3) |
| = | stochastic estimation | |
| σ | = | standard deviation |
| χ | = | interpolation weight in BWM |
| Greek symbols | = | |
| δ | = | spectral scattering coefficient (m−1) |
| ϵ | = | spectral absorptivity |
| κ | = | spectral absorption coefficient (m−1) |
| Superscripts | = | |
| A, E, O | = | ARM, ERM and ORM |
| B | = | BWM |
| F, R | = | FM and RM |
| S | = | quantity of surface cells |
| 0 | = | black body |
| V | = | quantity of volumetric cells |
| Subscripts | = | |
| i, j | = | elementary cell number |
| ν | = | spectral location (cm−1) |