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High-order conservative formulation of viscous terms for variable viscosity flows. (English) Zbl 1489.76038

Summary: 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.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N06 Compressible Navier-Stokes equations
76R50 Diffusion
76F10 Shear flows and turbulence
76F65 Direct numerical and large eddy simulation of turbulence
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