Dense suspensions of particles dispersed in liquids are central to industrial and geophysical processes and serve as model systems for out-of-equilibrium soft matter. At high particle concentrations, they exhibit stress-dependent rheology, including discontinuous shear thickening and shear jamming, arising from frictional contacts. Nonlinear physics arises from the interplay among direct contacts, interfacial chemistry, and fluid-mediated hydrodynamics. The relative importance of these mechanisms depends on the particle properties and flow conditions, making predictive modeling inherently multi-scale and, therefore, computationally challenging. Recent advances in computational methods have transformed our ability to simulate the physics of dense suspensions across different scales. In this Perspective, we primarily focus on state-of-the-art simulation frameworks that integrate the mechanics of dry granular materials, mediated by contact friction, with suspension hydrodynamics to provide predictive models of dense suspension rheology. We highlight recent computational developments for simulating dense, predominantly non-Brownian suspensions in the viscous limit at varying levels of fidelity, ranging from particle-resolved to continuum models, as well as models that investigate their mesoscale organization during flow. Together, these approaches reveal a hierarchical structure in which microscale constraints give rise to mesoscale frictional networks that ultimately govern the macroscopic flow. While our emphasis is on dense suspensions governed by near-field hydrodynamics and frictional interactions, we also briefly discuss complementary grid-based methods that can account for complex geometries and particle properties, and also enable continuum-scale descriptions.
Ayar et al. (Mon,) studied this question.