The work presents a general strategy to design high-order conservative co-located finite-difference approximations of viscous/diffusion terms for flows featuring extreme variations of diffusive properties. The proposed scheme becomes equivalent to central finite-difference derivatives with corresponding order in the case of uniform flow properties, while in variable viscosity/diffusion conditions it grants a strong preservation and a proper telescoping of viscous/diffusion terms. Presented tests show that standard co-located discretisation of the viscous terms is not able to describe the flow when the viscosity field experiences substantial variations, while the proposed method always reproduces the correct behaviour. Thus, the process is recommended for such flows whose viscosity field highly varies, in both laminar and turbulent conditions, relying on a more robust approximation of diffuse terms in any situation. Hence, the proposed discretisation should be used in all these cases and, for example, in large eddy simulations of turbulent wall flows where the eddy viscosity abruptly changes in the near-wall region.

这项工作提出了一种通用策略，为具有扩散特性极端变化的流动设计粘性/扩散项的高阶保守同位有限差分近似。在均匀流动特性的情况下，所提出的方案等效于具有相应阶数的中心有限差分导数，而在可变的粘度/扩散条件下，它可以很好地保持粘性和扩散性。提出的测试表明，当粘度场发生实质性变化时，粘性术语的标准共处离散化无法描述流量，而所提出的方法始终能够再现正确的行为。因此，对于层流和湍流条件下粘度场变化很大的此类流动，建议使用此方法，在任何情况下都依赖于扩散项的更鲁棒近似。因此，建议的离散化方法应在所有这些情况下使用，例如，在湍流壁流的大型涡流模拟中，其中涡流粘度在近壁区域会突然变化。