Discrete transfer method

An alternative approach similar to the discrete transfer method was reported by Taniguchi et al. [115,116,117]. They showed that, for nonscattering media, the method yields very good results with significant computational time savings over standard Monte Carlo techniques. 

Flux methods Multi flux approaches Discrete transfer method Discrete ordinates approx. 

For the solution of RTE a variant of the discrete transfer method adjusted to consideration of axisymmetric problems in complex domains is used. The method is based on the numerical integration of the RTE along the specified directions... 

Stamnes, K S.-C. Tsay, W. Wiscombe, and K. Jayaweera, Numerically Stable Algorithm for Discrete-Ordinate-Method Radiative Transfer in Multiple Scattering and Emitting Layered Media, Appl. Opt., 27, 2502-2509 (1988). 

Stammes K., Tsay S., W. Wiscombe and K. Jayaweera, Numerical stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media, Applied Optics 27, 2502-... 

Fiveland, W. A. and Jamaluddin, A. S. (1991). Three-Dimensional Spectral Radiative Heat Transfer Solutions by the Discrete-Ordinate Method. J. Thermophysics, 5, 335. 

Collin, A., Boulet, P., Lacroix, D., and Jeandel, G. On radiative transfer in water spray curtains using the discrete ordinates method. Journal of Quantitative Spectroscopy Radiative Transfer, 2005. 92, 85-110. 

In particular, Cabrera et al. (1996), Brandi et al. (1999), and Satuf et al. (2005) have determined optical parameters for Ti02 particles of several commercial brands. The determinations were carried out by means of spectrophotometry experiments involving the measurement of specular reflectance and beam transmittance, as well as hemispherical transmittance and reflectance, of catalyst suspensions (Cabrera et al., 1996). By radiative transfer calculations with the discrete ordinates method (DOM), the values of the extinction and absorption coefficient and of the asymmetry parameter that better fitted the results of measurements were found. Actually, the extinction coefficients of Satuf et al. (2005) are the same as those of Brandi... 

Several analytic methods have been proposed to solve the equation of radiative transfer in an absorbing and scattering atmosphere, but they can only be applied for the most simple cases. To obtain quantitative solutions, numerical methods are generally used, such as the Monte-Carlo method, DART method, iterative Gauss, discrete ordinate method, etc. A complete summary of these techniques is provided by Lenoble (1977), and a detailed discussion of multiple scattering processes in plane parallel atmospheres is given in the book by Liou (2002). 

Cameron, R.G., Marcos, R.L. and de Prada, C. (1998). Model validation of discrete transfer functions using the distortion method. Mathematical tmd Computer Modelling of Dytm-mica Systems, 4. 58-72. 

W. A. Fiveland, A Discrete-Ordinates Method for Predicting Radiative Heat Transfer in Axisymmetric Enclosures, ASME paper No. 82-HT-20, ASME, New York, 1982. 

W. A. Fiveland, Three-Dimensional Radiative Heat-Transfer Solutions by the Discrete-Ordinates Method, AIAA Journal of Thermophysics and Heat Transfer, 2, pp. 309-316,1988. 

A. S. Jamaluddin and P. J. Smith, Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method, Combustion Science and Technology, 62, p. 173,1988. 

W. A. Fiveland and J. P. Jessee, A Finite Element Formulation of the Discrete-Ordinate Method For Multidimensional Geometries, in Radiative Heat Transfer Current Research, ASME HTD no. 244, New York, 1993. 

J. C. Chai and S. V. Patankar, Evaluation of Spatial Differencing Practices for the Discrete Ordinates Method, AlAA Journal of Thermophysics and Heat Transfer, vol. 8, pp. 140-144,1994. 

W. Krebs, S. Wittig, and R. Viskanta, A Parabolic Formulation of the Discrete Ordinates Method for the Treatment of Complex Geometries in M. P. Mengii (ed.). Radiative Transfer—I Proceedings of the First International Symposium on Radiative Transfer, pp. 355-371, Begell House, New York, 1996. 

N. Selfuk and N. Kayakol, Evaluation of Angular Quadrature and Spatial Differencing Schemes for Discrete Ordinates Method in Rectangular Furnaces, in R. D. Skocypec, S. T. Thynell, D. A. Kaminski, A. M. Smith, and T. Tong (eds.), Solution Methods for Radiative Transfer in Participating Media, ASME HTD vol. 325, ASME, New York, 1996. 

N. Selkirk and N. Kayakol, Evaluation of Discrete Ordinates Method for Radiative Transfer in Rectangular Furnaces, International Journal of Heat and Mass Transfer, 40(2), pp. 213-222,1997. 

Most of the sample-transfer methods for microfluidic chips described above have been used to either inject discrete samples into a separation lane on a microchip or perform repeated injections of a single sample. Between analyses of different samples, the reservoirs and... 

Liu H., Chen W.S., Feng X T, Chen Q.R. 2004. Numerical modeling of daye iron open-pit-mine transferring to underground mining by discrete element method. Rock and Soil Mechanics 25(9) 1413-1417. 

The system can be first transformed into its state space form (2.1.12). The state space form describes the system s dynamic behavior in minimal coordinates. Discretizing this system by the same method leads to a discrete transfer matrix S h) of the state space form. 

---