Fast multiple-fluid simulation using Helmholtz free energy

Abstract

Figure 1: Egg Mixture. In simulating the stirring of 3 eggs by a blender, the resulting simulation presents visually plausible mixing results. This mixing effect is achieved using our novel "extended mobility" formulation of the Navier-Stokes-Cahn-Hilliard Model. AbstractMultiple-fluid interaction is an interesting and common visual phenomenon we often observe. In this paper, we present an energybased Lagrangian method that expands the capability of existing multiple-fluid methods to handle various phenomena, such as extraction, partial dissolution, etc. Based on our user-adjusted Helmholtz free energy functions, the simulated fluid evolves from high-energy states to low-energy states, allowing flexible capture of various mixing and unmixing processes. We also extend the original Cahn-Hilliard equation to be better able to simulate complex fluid-fluid interaction and rich visual phenomena such as motionrelated mixing and position based pattern. Our approach is easily integrated with existing state-of-the-art smooth particle hydrodynamic (SPH) solvers and can be further implemented on top of the position based dynamics (PBD) method, improving the stability and incompressibility of the fluid during Lagrangian simulation under large time steps. Performance analysis shows that our method is at least 4 times faster than the state-of-the-art multiple-fluid method.Examples are provided to demonstrate the new capability and effectiveness of our approach.

A unified particle system framework for multi-phase, multi-material visual simulations

“…Park et al [2008] showed that energy can be used to drive multi-fluid simulations, and adopted the Cahn-Hilliard equation to handle both miscible and immiscible fluids using a lattice Boltzmann method (LBM). Their approach was later extended by Yang et al [2015], who achieved impressive results for problems such as extraction (i.e. separating a substance from a mixture) and mixing of an egg yolk and egg white.…”

“…In this section, we first review the energy-driven multi-fluid simula-tion proposed by Yang et al [2015], and then show how to extend this framework to handle other phases.…”

“…Solenthaler and Pajarola [2008] simulated fluids using density contrast. By adopting the concept of volume fraction [Müller et al 2005], Ren et al [2014] and Yang et al [2015] managed to capture a wide range of multi-fluid flow phenomena with rich visual effects, using a mixture model and Helmholtz free energy. They focused on interactions between multiple fluids, and solids were not considered.…”

“…Yan et al [2016] extended the multi-fluid SPH framework to incorporate solids, achieving impressive results. However, their method is based on drift velocity, which requires small time steps, and cannot easily or intuitively capture the evolution of phenomena based on energy considerations [Yang et al 2015]. Furthermore, it cannot simulate phase-change phenomena such as melting and solidification.…”

“…Our approach significantly extends the energy-based multi-fluid approach proposed by Yang et al [2015] to represent 'solid' phases, enabling modeling of a variety of fluid-solid interactions. We treat phases and materials independently, thereby the unified multi-material simulation framework can model a much wider range of real-world phenomena.…”