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

湍流及其相关现象（如燃烧）的直接数值模拟（DNS）仍然是数学和物理科学中最大的挑战之一。所涉及的长度和时间尺度的范围是显着的，与极快的，精细结构的，多物种的反应过程与大尺度湍流运动的非线性相互作用。高阶数值方法可以提供有效的解决方案，但目前的方法是基于高阶有限差分或（伪）谱方法，这是不适合复杂的几何形状，因此真实的湍流应用的研究是非常有限的。高阶数值格式的非平凡的几何形状的发展是明确的数字建模和燃烧社区的好处。该项目的目的是开发一个有前途的新的无网格框架的任意复杂的几何形状的湍流反应流的高阶DNS。高阶无网格方法的最新发展-局部各向异性基函数方法（LABFM）-在提供相当大的几何灵活性以及高阶精度（例如空间中的10阶）方面显示出希望。这项可行性研究的目的是为下一代DNS代码奠定基础，在无网格的框架，使火焰湍流结构相互作用的模拟迄今不可能。从长远来看，这将导致对湍流反应流的基础和应用的更好理解，并将支持相关技术的发展，例如规模制氢，清洁燃烧和低热气体利用。

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.