We propose Monolith, a monolithic pressure-viscosity-contact solver formore accurately, robustly, and efficiently simulating non-trivial two-wayinteractions of rigid bodies with inviscid, viscous, or non-Newtonian liquids.Our solver simultaneously handles incompressibility and (optionally) implicitviscosity integration for liquids, contact resolution for rigid bodies,and mutual interactions between liquids and rigid bodies by carefully formulatingthese as a single unified minimization problem. This monolithicapproach reduces or eliminates an array of problematic artifacts, includingliquid volume loss, solid interpenetrations, simulation instabilities, artificial"melting" of viscous liquid, and incorrect slip at liquid-solid interfaces. Inthe absence of solid-solid friction, our minimization problem is a QuadraticProgram (QP) with a symmetric positive definite (SPD) matrix and can betreated with a single Linear Complementarity Problem (LCP) solve. Whenfriction is present, we decouple the unified minimization problem into twosubproblems so that it can be effectively handled via staggered projectionswith alternating LCP solves.We also propose a complementary approach fornon-Newtonian fluids which can be seamlessly integrated and addressed duringthe staggered projections. We demonstrate the critical importance of acontact-aware, unified treatment of fluid-solid coupling and the effectivenessof our proposed Monolith solver in a wide range of practical scenarios.
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