High-order conservative formulation of viscous terms for variable viscosity flows

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