Real-time fluid simulation using discrete sine/cosine transforms

Recent advances in fluid simulations have yielded exceptionally realistic imagery. However, most algorithms have computational requirements that are prohibitive for real-time simulations. Using Fourier based solutions mitigates this issue, although due to wraparound, boundary conditions are not naturally available, leading to inconsistencies near the boundary. We show that slip boundary conditions can be imposed by solving the mass conservation step using cosine and sine transforms instead of the Fourier transform. Further, we show that measures against density dissipation can be computed using cosine transforms and we describe a new method to compute surface tension in the same domain. This combination of related algorithms leads to real-time simulations with boundary conditions.