DOI: 10.1111/cgf.12467 COMPUTER GRAPHICS forum Volume 34 (2015), number 1 pp. 191–204 Stable and Fast Fluid–Solid Coupling for Incompressible SPH X. Shao 1 , Z. Zhou 1, ∗ , N. Magnenat-Thalmann 2 and W. Wu 1 1 State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China 2 Institute for Media Innovation, Nanyang Technological University, Singapore Abstract The solid boundary handling has been a research focus in physically based fluid animation. In this paper, we propose a novel stable and fast particle method to couple predictive–corrective incompressible smoothed particle hydrodynamics and geometric lattice shape matching (LSM), which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences. By combining the boundary particles sampled from solids with a momentum-conserving velocity-position correction scheme, our approach can alleviate the particle deficiency issues and prevent the penetration artefacts at the fluid– solid interfaces simultaneously. We further simulate the stable deformation and melting of solid objects coupled to smoothed particle hydrodynamics fluids based on a highly extended LSM model. In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs using compute unified device architecture. The advantages of our two-way fluid–solid coupling method in computer animation are demonstrated via several virtual scenarios. Keywords: fluid modelling, point-based animation, physically based animation ACM CCS: I.3.3 [Computer Graphics]: Three-Dimensional Graphics and Realism Animation 1. Introduction Physically based simulations of the fluid motions have been widely used for many applications, such as commercial films and computer games. Among various fluid motions, fluid–solid couplings happen all the time due to the flow characteristics inherent to the fluids. Although great progress has been made in fluid–solid couplings [BBB07, BTT09, KWC*10, AIA*12], especially for the interac- tions between fluids and deformable objects [MST*04, CGFO06, RMSG*08, ACAT13], certain difficulties still prevail and need to be resolved for particle-based smoothed particle hydrodynamics (SPH) fluids. First, it is still hard to meet the stability well at the fluid–solid coupling interfaces. To our knowledge, the stable boundary han- dling of SPH fluids needs to simultaneously address two open issues: the penetration artefacts [MST*04, YLHQ12, ACAT13] under larger time steps or velocity differences, and the particle deficiency issues [SB12, AIA*12] including density discontinu- ities and particle stacking due to the lack of fluid neighbours. The ∗ Corresponding author: Z. zhou (zz@vrlab.buaa.edu.cn) common penalty force methods [MST*04, HKK07, YLHQ12] pre- vent penetrations by using stiff boundary forces, but the fluid density and pressure at the interfaces are not estimated correctly. Further- more, the requirement of large penalty forces for non-penetration restricts the time step. The direct forcing method [BTT09] adopts a predictor–corrector scheme to compute coupling forces and ve- locities, and guarantees non-penetration under larger time steps, but particle stacking occurs at the interfaces. The particle deficiency issues can be alleviated by considering the contributions of mir- ror particles [MM97, HA06, SB12] or frozen particles [SSP07, IAGT10, AIA*12] to fluid particles. However, the effectivity of these methods in penetration prevention is determined by the sam- pling density of mirror particles or frozen particles. Although Akinci et al. [ACAT13] adaptively sample the surfaces of de- formable objects with relatively contributive boundary particles to prevent undesired leakage, it is hard to determine a suitable sampling density of boundary particles for non-penetrations in the case of larger time steps or velocity differences. To alleviate the particle deficiency issues, we sample the objects with both surface boundary particles (SBPs) and inner boundary particles (IBPs), and consider their relative contributions to the fluid particles in different ways. In combination with a momentum-conserving velocity-position correction scheme suitable for our boundary c  2014 The Authors Computer Graphics Forum c  2014 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 191