A Fast Iterated Orthogonal Projection Framework for Smoke Simulation

We present a fast iterated orthogonal projection (IOP) framework for smoke simulations. By modifying the IOP framework with a different means for convergence, our framework significantly reduces the number of iterations required to converge to the desired precision. Our new iteration framework adds a divergence redistributor component to IOP that can improve the impeded convergence logic of IOP. We tested Jacobi, GS and SOR as divergence redistributors and used the Multigrid scheme to generate a highly efficient Poisson solver. It provides a rapid convergence rate and requires less computation time. In all of our experiments, our method only requires 2-3 iterations to satisfy the convergence condition of 1e-5 and 5-7 iterations for 1e-10. Compared with the commonly used Incomplete Cholesky Preconditioned Conjugate Gradient(ICPCG) solver, our Poisson solver accelerates the overall speed to approximately 7- to 30-fold faster for grids ranging from
$128^3$
to
$256^3$
. Our solver can accelerate more on larger grids because of the property that the iteration count required to satisfy the convergence condition is independent of the problem size. We use various experimental scenes and settings to demonstrate the efficiency of our method. In addition, we present a feasible method for both IOP and our fast IOP to support free surfaces.