The objective of this work is to propose to the urban physics community an optimal sky vault partition able to support most existing applications, either in daylight availability evaluation or in shortwave energy budget estimation. This partition is explained and justified. Its refinement is examined and analysed with respect to the studies performed today at urban level. The solution of the analyses is obtained in two steps: the heaviest part is the solution of the urban interreflection problem, while the second step is very fast and can be achieved in interactive mode. It consists in computing the thermal or illumination loads which will be used as coefficients of a recombination of the first step results. The urban interreflection problem is independent of this process and can be obtained with various existing techniques, such as the radiosity method.
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References
1.
PettyGW. A First Course on Atmospheric Radiation, 2nd. Madison WI: Sundog, 2006.
2.
CompagnonR. Solar and daylight availability in the urban fabric. Energy and Buildings2004; 36: 321–328.
3.
Robinson D, Stone A. Irradiation modelling made simple:The cumulative sky approach and its applications: Proceedings of the 21st Conference on Passive and Low Energy Architecture, Eindhoven, The Netherlands, Sep 19–22: 2004.
4.
RobinsonD. Computer Modelling for Sustainable Urban Design. Physical Principles, Methods and Applications, London: Earthscan, 2011.
5.
Mardaljevic J, Janes GM. Multiscale daylight modeling for urban environment. In Beckers B, editor. Solar Energy at Urban Scale. 2012: 159–190. Great Britain and US: ISTE Ltd and John Wiley & Sons, Inc.
6.
Commission Internationale de l’Eclairage. Guide to Recommended Practice of Daylight Measurement. CIE Publication 108-1994, Vienna: CIE, 1994.
van Eekelen T. Radiation modeling using the finite element method. In Beckers B, editor. Solar Energy at Urban Scale, 2012: 237–257. Great Britain and US: ISTE Ltd and John Wiley & Sons, Inc.
9.
GrimmondCSBPotterSKZutterHNSouchC. Rapid methods to estimate sky-view factors applied to urban areas. International Journal of Climatology2001; 21: 903–913.
10.
SillionFPuechC. Radiosity and Global Illumination, San Francisco: Morgan Kaufmann, 1994.
11.
GeebelenBvan der VoordenMNeuckermansH. Fast and accurate simulation of long-term daylight availability using the radiosity method. Lighting Research and Technology2005; 37: 295–312.
12.
AmestoyPRDuffISL’ExcellentJ-YRobertYRouetF-HUçarB. On computing inverse entries of a sparse matrix in an out-of-core environment. SIAM Journal on Scientific Computing2012; 34: A1975–A1999.
13.
GuptaA. Recent advances in direct methods for solving unsymmetric sparse systems of linear equations. ACM Transactions on Mathematical Software,2002; 28: 301–324.
14.
LiXSDemmelJW. SuperLU_DIST: Distributed-Memory Sparse Direct Solver for unsymmetric linear systems. ACM Transactions on Mathematical Software2003; 29: 110–140.
15.
Beckers B, Beckers P. Radiative simulation methods. In Beckers B, editor. Solar Energy at Urban Scale, 2012: 205–236. Great Britain and US: ISTE Ltd and John Wiley & Sons, Inc.
16.
Miguet F. Paramètres physiques des ambiances architecturales: Un modèle numérique pour la simulation de la lumière naturelle dans le projet urbain. PhD thesis. Nantes: École Polytechnique de l’Université de Nantes, École d’Architecture de Nantes, 2000.
17.
Marsh A. The application of shading masks in building simulation: Proceedings of the Ninth International IBPSA Conference, Montréal, Canada, Aug 15–18: 2005.
18.
BeckersBBeckersP. A general rule for disc and hemisphere partition into equal-area cells. Computational Geometry2012; 45: 275–283.
19.
FreyPJGeorgePL. Mesh Generation Application to Finite Elements, London: ISTE Ltd, 2008.
20.
BeckersBMassetLBeckersP. The universal projection for computing data carried on the hemisphere. Computer-Aided Design2011; 43: 219–226.
21.
WooldridgeCHaymanS. Cloud cover assessment grids for whole-sky images. Lighting Research and Technology1994; 26: 9–12.
22.
TregenzaPR. Subdivision of the sky hemisphere for luminance measurements. Lighting Research and Technology1987; 19: 13–14.
23.
Beckers B. Taking advantage of low radiative coupling in 3D urban models: Proceedings of Eurographics Workshop on Urban Data Modelling and Visualization, Gerona, May 5: 2013.
