A fast variational framework for accurate solid-fluid coupling

Abstract

Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a wellposed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the framework with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.

Ghost SPH for animating water

“…This naturally enforces the no-penetration and no-separation boundary condition (up to numerical errors). Note that while this is physically correct, when the boundary layer is under-resolved, as may happen in large-scale simulations, reverting to freely separating boundary conditions by disallowing negative pressures may provide more plausible results [Batty et al 2007;Chentanez and Müller 2011].…”

Simulation of Fluid and Complex Obstacle Coupling Based on Narrow Band FLIP Method

“…The transition from gird to particles are handled by sharp transition as shown in Equation (5). The reader are suggested to refer to reference [3] for more detailed discussion.…”

“…Zhu [4] introduced the FLIP and PIC (Particle in Cell) methods into the computer graphics community in sand simulation, in which the sticky effect of sand flow was reproduced successfully. Batty [5] proposed a fluid-solid coupling method based on variational principles and solved problems on interaction with slim obstacles. Cornelis [6] and Zhu [7] combined FLIP method with Smoothed Particle Hydrodynamics (SPH) method for incompressible fluid simulation with an expectation of getting more details.…”

Fluid Simulation with Articulated Bodies

“…Guendelman et al [13] use a similar object velocity/fluid pressure coupling to animate the interaction of incompressible fluids with zero volume deformable and rigid shells. [3], [15]- [17] solve simultaneosly for the fluid pressure and solid velocity to obtain a fully implicit two-way solid-fluid coupling. We chose to use the Rigid Fluid method from Carlson et al [9] to model our rigid bodies interacting with incompressible fluid.…”

“…In these situations the object does not cause any changes to the water. Only recently have we seen animations where the motion of the object affects the fluid and vice-versa [3], [9], [12]- [17]. We use a full two-way solid-fluid coupling enabling us to demonstrate effects that were not viable before.…”