High-order matrix-free methods for dense particle-laden flows: An open-source perspective

Abstract: The simulation of flows using computational fluid dynamics (CFD) has advanced considerably in recent decades and is now an essential tool across industries ranging from aerospace design to process engineering. Although CFD is relatively mature for single-phase flows, particle-laden flows remain significantly more challenging to simulate, in part due to their intrinsic multiscale nature: particle–fluid interactions at the particle length scale propagate across all length scales. Inherently opaque, these flows are extremely difficult to study experimentally, and simulation remains one of the most viable strategies for gaining insight into their internal dynamics. Among the wide variety of simulation models for particle-laden flows, Euler–Lagrange approaches are particularly appealing owing to their capacity to describe individual rigid particles explicitly. Two main classes of Euler–Lagrange models can be distinguished: Resolved (REL) and Unresolved (UREL). Resolved models discretize the fluid equations at a scale finer than the particles and enforce the no-slip boundary condition at the solid–fluid interface, typically through an immersed boundary method. While accurate, this approach is highly computationally intensive, which limits the number of particles that can feasibly be simulated. Unresolved models instead filter the Navier–Stokes equations and treat particles as point momentum sources, greatly reducing the computational cost at the expense of requiring accurate closure models. This talk presents our efforts in designing Lethe, an open-source, high-order multiphysics framework for single- and multiphase flows built on the deal.II library. We first motivate the use of high-order finite elements for CFD applications in process engineering. After discussing the challenges associated with our high-order stabilized formulation, we introduce matrix-free methods as a paradigm that alleviates several of these difficulties. We then present the implementation of a matrix-free stabilized Navier–Stokes solver within Lethe and demonstrate its capabilities for turbulent flow simulations. Building on this foundation, we describe both our REL and UREL implementations for particle-laden flows and illustrate their capabilities through selected applications. For REL, we demonstrate the model’s ability to accurately capture the dynamics of individual particles by investigating the sedimentation of spherical and non-spherical bodies. For UREL, we show that this approach can simulate the dynamics of large numbers of particles in complex systems. We conclude by reflecting on the potential of high-order methods for particle-laden flows, the role of opensource software in developing accurate and efficient simulation tools for these complex systems, and some of the lessons learned during the development of Lethe. Finally, we outline future directions for this work, including the development of more accurate closure models for UREL and the extension of our framework to additional multiphysics applications.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)