Shape conservation of FFT-based smoke simulation

This paper introduces a novel method to conserve the shape of smoke simulation based on fast Fourier transform. Through the advection step of simulating Navier-Stokes equation, semi-Lagrange method loses the high frequency part of fluid, since the interpolation method is equal to low-pass filter, which causes the shape of fluids variable in different resolution. The method consists of the dissipation in advection step to conserve the shape of fluids by applying Laplace kernel in the advection step. In order to speed up the computing step, convolution of Laplace kernel is applied in the frequency filed through fast Fourier transform, which compensates the high frequency part of smoke´s self-advection to conserve the shape.