We present DIQ-MPM, a novel monolithic two-way coupling framework for simulating interactions between solids modeled with the total Lagrangian formulation and Eulerian incompressible fluids using the Material Point Method (MPM). Our approach combines an implicit TLMPM formulation with a mixed velocity-pressure scheme to robustly simulate compressible solids undergoing large deformations, while eliminating numerical fractures. To enable strong fluid-solid coupling without relying on overlapping grids, we introduce a Dual Interface Quadrature (DIQ) mechanism that maps fluid-solid interface information consistently between the current and reference configurations. This allows us to construct a unified sparse pressure-only system via Schur complement, leading to efficient and stable coupling. We also integrate a particle-based contact force model to resolve solid-solid and solid-boundary contacts within implicit TLMPM. Experimental results demonstrate that our method stably captures free-slip coupling, large deformation phenomena, and complex interactions between compressible solids and incompressible fluids.

Fluid flows in spherical coordinates have raised the interest of the graphics community in recent years. The majority of existing works focus on 2D manifold flows on a spherical shell, and there are still many unresolved problems for 3D simulations in spherical coordinates, such as boundary conditions for arbitrary obstacles and flexible artistic controls. In this article, we propose a practical spherical-coordinate simulator for flow motions in 3D domains. Based on a layer-by-layer structure and a boundary-aware pressure solving scheme, we are able to recover horizontal and vertical flow motions in the presence of arbitrary terrain shapes within a spherical shell of finite thickness. Our proposed method straightforwardly builds on the conventions of previous 2D-manifold spherical-coordinate simulations and provides flexible artistic control strategies for art design.