Deep ensembles assisted multiscale modeling of rheologically complex fluids

Continuum modeling of complex fluid dynamics without an explicitly-known constitutive rheology, such as the relationship between viscosity and local fluid flow state, relies on a multiscale methodology wherein particle-based simulations are used to either precompute the entire rheological space, or inform the local rheology for every fluid cell at each time step of the continuum fluid simulation. Both these approaches can quickly become computationally intractable, particularly since the rheological space to sample can be very large and is often a priori unknown in most scenarios. This study leverages ensemble deep learning to obtain an uncertainty quantified approximation of the intrinsic constitutive rheology. Our multiscale method reduces the need for numerous expensive particle-based simulations by adaptively focusing on the under-sampled rheological spaces with high-variance. Hence, reducing the computational expense and making the multiscale problem tractable.

We demonstrate the efficacy of this approach through continuum modeling of the dynamics of granular materials and suspensions with complex intrinsic rheology. We use this framework to investigate the effect of particle properties, such as interparticle friction and cohesion, on the macroscopic dynamics in various flow scenarios. We will highlight the accuracy of this integrated approach by comparing against particle-resolved methods, such as the discrete element method.