A Geometrically Consistent Viscous Fluid Solver with Two-Way Fluid-Solid Coupling.

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.