A High-Fidelity Methodology for Particle-Resolved Direct Numerical Simulations

TL;DR

This paper introduces a rigorous computational method for particle-resolved direct numerical simulations of particle-laden flows, using volume-filtering to control fidelity and unify resolved and point-particle approaches.

Contribution

The novel PR-DNS method based on volume-filtering immersed boundary technique offers a mathematically rigorous framework for simulating particle-laden flows with adjustable fidelity.

Findings

The filter size to particle diameter ratio controls simulation fidelity.

The method reduces to point-particle models at large filter sizes.

Numerical examples demonstrate the method's effectiveness in sedimenting particles.

Abstract

We present a novel computational method for direct numerical simulations of particle-laden flows with fully-resolved particles (PR-DNS). The method is based on the recently developed Volume-Filtering Immersed Boundary method [Dave et al, Journal of Computational Physics, 487:112136, 2023] derived by volume-filtering the transport equations. This approach is mathematically and physically rigorous, in contrast to other PR-DNS methods which rely on ad-hoc numerical schemes to impose no-slip boundary conditions on the surface of particles. With the present PR-DNS strategy, we show that the ratio of filter size to particle diameter acts as a parameter that controls the level of fidelity. In the limit where this ratio is very small, a well-resolved PR-DNS is obtained. Conversely, when the ratio of filter size to particle diameter is large, a classic point-particle method is obtained. The discretization of the filtered equations is discussed and compared to other PR-DNS strategies based on direct-forcing immersed boundary methods. Numerical examples with sedimenting resolved particles are discussed.