In this paper, we propose a new constrained interpolation profile (CIP) method that is stable and accurate but requires less amount of computation compared to existing CIP-based solvers. CIP is a high-order fluid advection solver that can reproduce rich details of fluids. It has third-order accuracy but its computation is performed over a compact stencil. These advantageous features of CIP are, however, diluted by the following two shortcomings: (1) CIP contains a defect in the utilization of the grid data, which makes the method suitable only for simulations with a tight CFL restriction; and (2) CIP does not guarantee unconditional stability. There have been several attempts to fix these problems in CIP, but they have been only partially successful. The solutions that fixed both problems ended up introducing other undesirable features, namely increased computation time and/or reduced accuracy. This paper proposes a novel modification of the original CIP method that fixes all of the above problems without increasing the computational load or reducing the accuracy. Both quantitative and visual experiments were performed to test the performance of the new CIP in comparison to existing fluid solvers. The results show that the proposed method brings significant improvements in both accuracy and speed.

This paper describes a motion blur technique which can be applied to rendering fluid simulations that are carried out in the Eulerian framework. Existing motion blur techniques can be applied to rigid bodies, deformable solids, clothes, and several other kinds of objects, and produce satisfactory results. As there is no specific reason to discriminate fluids from the above objects, one may consider applying an existing motion blur technique to render fluids. However, here we show that existing motion blur techniques are intended for simulations carried out in the Lagrangian framework, and are not suited to Eulerian simulations. Then, we propose a new motion blur technique that is suitable for rendering Eulerian simulations.

We present a new fluid simulation technique that significantly reduces the non-physical dissipation of velocity. The proposed method is based on an apt use of particles and derivative information. We note that a major source of numerical dissipation in the conventional Navier--Stokes equations solver lies in the advection step. Hence, starting with the conventional grid-based simulator, when the details of fluid movements need to be simulated, we replace the advection part with a particle simulator. When swapping between the grid-based and particle-based simulators, the physical quantities such as the level set and velocity must be converted. For this purpose, we develop a novel dissipation-suppressing conversion procedure that utilizes the derivative information stored in the particles as well as in the grid points. For the fluid regions where such details are not needed, the advection is simulated using an octree-based constrained interpolation profile (CIP) solver, which we develop in this work. Through several experiments, we show that the proposed technique can reproduce the detailed movements of high-Reynolds-number fluids, such as droplets/bubbles, thin water sheets, and whirlpools. The increased accuracy in the advection, which forms the basis of the proposed technique, can also be used to produce better results in larger scale fluid simulations.