Mesh-free methods for turbulent reacting flows: the next generation of DNS

The direct numerical simulation (DNS) of turbulence and related phenomena, e.g. combustion, remains one of the great challenges in the mathematical and physical sciences. The range of length- and time-scales involved is significant, with extremely fast, finely structured, many-species reaction processes interacting non-linearly with large-scale turbulent motions. High-order numerical methods can provide efficient resolution but current approaches are based on high-order finite differences or (pseudo-)spectral methods, which are not well suited to complex geometries, and hence the study of real turbulence applications is very limited. The development of high-order numerical schemes for non-trivial geometries is of clear benefit to the numerical modelling and combustion communities. The aim of this project is to develop a promising new mesh-free framework for high-order DNS of turbulent reacting flows in arbitrarily complex geometries. Very recent developments of a high-order mesh-free method - the Local Anisotropic Basis Function Method (LABFM) - show promise in providing considerable geometric flexibility as well as high-order accuracy (e.g. 10th order in space). The intention of this feasibility study is to lay the foundations for the next generation of DNS codes, in a meshless framework, enabling simulations of flame-turbulence-structure interactions hitherto impossible. In the longer term this will result in a greater understanding, both fundamental and in application, of turbulent reacting flows, and will support the development of related technologies, such as hydrogen production at scale, cleaner combustion, and low calorific gas utilisation.