• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.191-196
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• 2007

In the field of computer graphics, Navier-Stokes equations would be used for realistic simulations of smokes and currents. However, implementations derived from these equations are hard to achieve for real-time simulations, mainly due to its massive and complex calculations. Thus, there have been various attempts to approximate these equations for real-time simulation of smokes and others. When the advection terms of the equations are approximated by the Semi-Lagrange methods, the fluid density can be rapidly reduced and small-scale vorticity phenomena are easy to be missed, mainly due to the numerical losses over time. In this paper, we propose an improved numerical method to approximately calculate the advection terms, and thus eliminate these problems. To calculate the advection terms, our method starts to set critical regions around the target grid points. Then, among the grid points in a specific critical region, we search for a grid point which will be advected to the target grid point, and use the velocity of this grid point as its advection vector. This method would reduce the numerical losses in the calculation of densities and vorticity phenomena, and finally can implement more realistic smoke simulations. We also improve the overall efficiency of vector calculations and related operations through GPU-based implementation techniques, and thus finally achieve the real-time simulation.