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A Geometrically Consistent Viscous Fluid Solver with Two‐Way Fluid‐Solid Coupling
Author(s) -
Takahashi Tetsuya,
Lin Ming C.
Publication year - 2019
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13618
Subject(s) - solver , viscosity , viscous liquid , coupling (piping) , grid , boundary (topology) , computer science , mechanics , boundary value problem , position (finance) , range (aeronautics) , mathematical optimization , mathematics , physics , mathematical analysis , materials science , geometry , thermodynamics , finance , economics , metallurgy , composite material
We present a grid‐based fluid solver for simulating viscous materials and their interactions with solid objects. Our method formulates the implicit viscosity integration as a minimization problem with consistently estimated volume fractions to account for the sub‐grid details of free surfaces and solid boundaries. To handle the interplay between fluids and solid objects with viscosity forces, we also formulate the two‐way fluid‐solid coupling as a unified minimization problem based on the variational principle, which naturally enforces the boundary conditions. Our formulation leads to a symmetric positive definite linear system with a sparse matrix regardless of the monolithically coupled solid objects. Additionally, we present a position‐correction method using density constraints to enforce the uniform distributions of fluid particles and thus prevent the loss of fluid volumes. We demonstrate the effectiveness of our method in a wide range of viscous fluid scenarios.