Real-time Rendering of Gas Phenomena around Single Building

= − (U ⋅ ∇ )T
(3)
step, γ and β are constants value to indicate physical features of smoke, set by users, and Pj is the average density in the layer. Figure 1 and Figure 2 shows the result of rendering.
2008 Congress on Image and Signal Processing
Real-time Rendering of Gas Phenomena around Single Building
He Guo, Yuxin Wang, Jun Tang, Tianyang Liu Department of Computer Science, Dalian University of Technology, Dalian, China E-mail: wang_yuxin@ Abstract *
*
Supported by the National Natural Science Foundation of China under Grant No. 60675008
978-0-7695-3119-9/08 $25.00 © 2008 IEEE DOI 10.1109/CISP.2008.486
(4) = − (U ⋅ ∇ ) ρ ∂t Semi-Lagrangian stable fluids approach [1] is used to solve those above equations. Heavy smoke tends to fall downwards due to gravity while hot gases tend to rise due to buoyancy. The external buoyancy force is directly proportional to the density and the temperature, fbuoy = −αρ Z + β (T − Tamb ) Z where Z = (0, 0,1) points in the upward vertical direction and α, β are positive constant with appropriate units. Nonphysical numerical dissipation damps out interesting flow features, and we use vorticity confinement [3] to generate the swirling effects. First the vorticity ω = ∇ × U is identified as the source of small scale structure, and the normalized vorticity
Based on the real-time fluid simulating method in the field of volume and surface rendering, gas phenomena can be rendered by using semi-Lagrange algorithm in three-dimensional volume environment. Combined with the large eddy model of single building, simulation of turbulent wind field around building by simplified eddy model can decrease the complexity, and add details to render. The mirror reflection method of simulation the alternation between building and fluid can avoid the change caused by shape of the building. The rendering and simulation of gas phenomena around building has been accomplished at lower cost. turbulence around objects. Rendering of gas phenomena is not accurate in the area around buildings. For rendering gas phenomena in complex environment, one must simulate the local turbulence wind flow. In urban environment, the existence of buildings cause decrease of velocity of air flow and increase the turbulence around the buildings, which has obvious un-homogeneous structure [8]. Zhang et al [9] combined the large eddy model with random Lagrange model to simulate smoke in the transformative airflow, which caused by buildings. However, the unstable model costs too much time to simulate, and not fit for real-time rendering. In this study, we develop a new method to simulate smoke around single building by simulate the simplified large eddy model using semi-Lagrange method with octree data structure [6]. The smoke in wind field around building can be real-time rendered quite factually.
(η = ∇ | ω |) that point |η | from lower to higher concentrations of vorticity are constructed. The magnitude and direction of the vorticity confinement force is computed as fconf = ε h( N × ω ) where ε > 0 and is used to control the amount of small scale detail added back into the flow, and the dependence on the grid size h guarantees that the physically correct solution is obtained as the mesh is refined.
∇=( ∂ ∂x ∂y ∂z , ∂ , ∂ )
, and
U = (u , v, w) is the velocity field of fluid. p , f account for the pressure and the extern force. t 0 = 0 when simulate starts. Then the fluid’s tempura (T) and the density ( ρ ) are simulated, followed by their equations
location vectors, N =
η
Figure 1. Rendering of smoke without extern force. The size of grid is 120×120×60. The time step is 0.5s. Using average 10s per frame. Left is the 6th frame, and right is the 9th frame.
2. Real-time render
2.1 Three-dimensional incompressible fluid
Because the velocity of smoke is much smaller than sound, we treat smoke as incompressible fluis modeled with the threedimensional Euler equations known as Navier-Stokes equations ∇ ⋅U = 0 (1) ∂U (2) = − (U ⋅ ∇ )U − ∇p + f ∂t Where ∇ is Laplacian,
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∂T ∂t ∂ρ
Keywords: Semi-Lagrange; large eddy; real-time;
rendering
1. Introduction
With the positions of building and the air condition in urban environment, Real-time rendering of gas phenomena can be used to reproduce the real scenes in computer view. The technology has broad application such as digital city, digital entertainment environment protection, and virtual reality. In real-time fluid simulation field, J Stam [1] introduced semi-Lagrange algorithm to the computer graphics. Because of dissipation of semi-Lagrange [2], R Fedkiw et al [3] introduced a vorticity confinement [4] method to compensate the dissipation, and also add details to the flow. Rasmussen et al [5] used the semiLagrange method to simulate smoke in large scale. Then Losasso et al [6] use octree data structure to store the grid, which can be used for irregular object [7]. However, these methods do not consider about local