A low-dissipative, scale-selective discretization scheme for the Navier–Stokes equations

A new Scale-Selective Discretization (SSD) procedure for the Navier–Stokes equations is proposed. The aim is to reduce the numerical dissipation of already existing numerical schemes to make the SSD scheme easily implementable to the existing CFD codes. In particular, the new procedure is designed to decrease the dissipation errors arising from the discretization of the convection term using upwind-biased convection schemes. Such dissipative errors reduce the quality of high-fidelity simulation approaches in fluid dynamics such as Large-Eddy Simulations (LES). The new discretization procedure is based on separating small and large scales of the flow using a high-pass filter. As a first pre-processing step the convecting velocity field uiui is decomposed into a rapidly fluctuating part ui′ using the high-pass filter and a smooth part ui-ui′. After this the derivatives involving ui-ui′ may be discretized with a centered scheme whereas the derivatives involving ui′ can be discretized using an upwind method. The new procedure is tested in Navier–Stokes simulations by implementing the method into a second order accurate incompressible finite volume code based on the fractional step method. The numerical tests on the 2D lid-driven cavity at laminar conditions Re=2500Re=2500 imply that the new method clearly improves the quality of the simulations. At Re = 10,000 the SSD scheme captures the post-critical state of the cavity flow. The advantages of the new method are quantitatively assessed by studying a 2D temporally evolving shear layer. The results imply that the SSD scheme significantly reduces the numerical diffusion in contrast to the conventional upwind-biased schemes. Results from marginally resolved turbulent channel flow at Reτ=590Reτ=590 imply that the new scheme can be used for 3D simulations.

► A new method to reduce diffusion errors of already existing upwind biased schemes is given.
► The new SSD method is easy to implement to any existing code.
► E.g. first order diffusive error of an upwind method would become third order with SSD.
► The SSD scheme can reduce dissipation of basic schemes by more than an order of magnitude.
► The scheme gives improved results in 2D and 3D flow cases including turbulent channel flow.