Local kinetic sensors for adaptive mesh and algorithm refinement

TL;DR

This paper introduces new local refinement sensors for adaptive mesh refinement in kinetic models like lattice Boltzmann methods, enabling scalable and accurate simulations of complex fluid flows.

Contribution

It presents a novel set of refinement sensors leveraging one-particle distribution functions for improved adaptive mesh refinement in kinetic fluid simulations.

Findings

Validated sensors for compressible, viscous, non-equilibrium flows

Demonstrated improved accuracy and scalability in kinetic simulations

Showcased application to a discrete velocity Boltzmann solver

Abstract

This paper presents novel refinement sensors for the application to adaptive mesh and algorithm refinement (AMAR) with kinetic models, such as discrete velocity and lattice Boltzmann methods. While refinement criteria for AMAR based on macroscopic variables can be replicated in a purely local, and therefore more scalable, way, the main advantage that can be leveraged when working with discrete velocity and lattice Boltzmann methods is the accessibility of information from the one-particle distribution function. With this accessibility, a novel palette of refinement sensors is introduced, allowing for a set of neatly tailored refinement criteria applicable to resolve characteristic flows features in many relevant domains of fluid mechanics, for instance, those emerging in compressible, turbulent, and non-equilibrium flows or non-ideal fluids. After detailed validation, novel refinement sensors are showcased for the application of adaptive mesh refinement (AMR) to a discrete velocity Boltzmann solver for compressible, viscous, and non-equilibrium flows, demonstrating promising results. The proposed sensors establish an accurate, efficient and scalable approach to kinetic simulations with AMAR, offering a valuable tool for studying complex problems in fluid dynamics and paving the way for future extensions to more specific flow problems.