Narrow Results

Unsteady flows in the field of engineering are usually calculated by the Unsteady Reynolds-Averaged Navier–Stokes (URANS) owing to the low requirements for computational efforts. However, the numerical resolution of URANS, especially in predicting the unsteady wake flows and sound, is still questionable. In this work, unsteady flow and sound calculations of a circular cylinder are carried out using Improved Delayed Detached Eddy Simulation (IDDES) and the Ffowcs Williams–Hawkings (FW-H) analogy. The predicted results of this calculation are compared with those from the previous studies in the literature in terms of the mean and RMS of the velocity components as well as the sound pressure. The results show that IDDES retains much of the numerical accuracy of the Large Eddy Simulation (LES) approach in predicting unsteady flows and noise while requiring a reduced computational resources in comparison to LES. It is believed that the IDDES can be applied to calculate the complex unsteady flows and flow generated sound with reasonable accuracy in engineering field, which can be used as a promising method for scale-resolving simulations to avoid the expensive computational requirements of LES.

We consider functions u ∈ L^∞(L²)∩L^p(W^{1, p}) with 1 < p < ∞ on a time–space domain. Solutions to nonlinear evolutionary PDEs typically belong to these spaces. Many applications require a Lipschitz approximation u_λ of u which coincides with u on a large set. For problems arising in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we construct a Lipschitz approximation, which is also solenoidal. As an application we revise the existence proof for non-stationary generalized Newtonian fluids of Diening, Ruzicka and Wolf, Existence of weak solutions for unsteady motions of generalized Newtonian fluids, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010) 1–46. Since divu_λ = 0, we are able to work in the pressure free formulation, which heavily simplifies the proof. We also provide a simplified approach to the stationary solenoidal Lipschitz truncation of Breit, Diening and Fuchs, Solenoidal Lipschitz truncation and applications in fluid mechanics, J. Differential Equations253 (2012) 1910–1942.