K-41 optimised approximate deconvolution models
Summary: Average the Navier-Stokes equations, with a local, spatial convolution type filter. The result system is not closed due to \(\overline {uu}\). Let \(D\) be a bounded linear operator which satisfies \[ \mathbf u = D(\overline{u}) + O(\delta ^{\alpha}), \] where \(\delta \) is the filter width and \(\alpha \geq 2\). Using \(D\) as an approximate filter inverse yields the closure \[ {\overline {uu}} = \overline {D(\overline {u})D(\overline {u})}+O(\delta ^{\alpha }). \] The residual stress of this model (and related models) depends directly on the deconvolution error \(\mathbf u - D(\overline{u})\). We find deconvolution parameters that minimise the deconvolution error for homogeneous, isotropic turbulence. This work addresses: How to adapt deconvolution to homogeneous, isotropic turbulent flows? And what is the increase in accuracy?
scientific article; zbMATH DE number 5703888
scientific article