A mesh-free framework for high-order direct numerical simulations of combustion in complex geometries

TL;DR

This paper introduces a high-order mesh-free DNS method for simulating turbulent combustion in complex geometries, overcoming limitations of traditional grid-based approaches and enabling more realistic simulations.

Contribution

A novel high-order mesh-free discretisation approach for DNS of combustion, capable of handling complex geometries with accuracy comparable to finite difference methods.

Findings

Validates the method against laminar and turbulent flows

Successfully captures unsteady bluff body flames

Qualitative agreement with published data on flame-turbulence interactions

Abstract

The multiscale nature of turbulent combustion necessitates accurate and computationally efficient methods for direct numerical simulations (DNS). The field has long been dominated by high-order finite differences, which lack the flexibility and adaptivity for simulations of complex geometries and flame-turbulence-structure interactions in realistic settings. In this work we introduce a new approach to DNS of premixed combustion, based on a high-order mesh-free discretisation in combination with finite differences, enabling high-order simulations in non-trivial geometries. The approach is validated against a range of two- and three-dimensional flows, both laminar and turbulent, and reacting and inert. The present method a) has the resolving power for DNS of both laminar flames and inert turbulence with comparable accuracy to high-order finite differences, b) can capture the dynamics of unsteady bluff body stabilised flames, and c) is capable of simulating flame-turbulence interactions, with results comparing qualitatively well with published data. This work paves the way for DNS of combustion in complex geometries, offering an alternative approach to methods based on structured grids with immersed boundaries, or unstructured meshes. Further studies with the present method are proposed, which will aid understanding of fundamental flame dynamics in non-trivial geometries. Planned developments in adaptivity and extension of the mesh-free construction to all three dimensions will increase the value of the method, and support the push towards DNS of real geometries.