The Fourier decomposition and the anisotropic diffusion filtering model are used to extract various flow field scales and their coherent and incoherent parts. The different flow field scales are identified using the Fourier decomposition. Three cutoff wavenumbers are chosen to extract large, medium and fine scale velocity fields, respectively. Then, the anisotropic diffusion model is applied against the obtained velocity fields for each scale to define the coherent and incoherent parts. The forced turbulent velocities are simulated using the lattice Boltzmann method with resolutions [Formula: see text] and [Formula: see text], respectively. The Fourier decomposition of the velocity fields make the filtering process very difficult, so the anisotropic diffusion parameters should be chosen carefully to overcome the problems arising from the sharp cutoffs process. Although of such difficulties, results show that the anisotropic diffusion model successfully isolate the incoherent parts for each scale. It is shown that the incoherent parts are existed everywhere in the flow fields and they are not limited to the fine scales. The coherent fields that are identified by the anisotropic diffusion filtering method are found similar to the extracted scales by the Fourier decomposition. The incoherent regions are fewer in the large scale fields compared with that found in the intermediate and fine fields. The statistical characteristics of the three flow field scales as well as their coherent and incoherent parts are studied and compared with the universal characteristics of turbulence.
We proposed an efficient local differential quadrature method which is based on the radial basis function to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. The explicit time integration technique is utilized to semi-discretize the model in the time direction whereas the space derivatives of the model is discretized by the proposed local meshless procedure based on multiquadric radial basis function. Numerical experiments on ve test problems are performed with the proposed numerical scheme for rectangular and non-rectangular computational domains. The results obtained show that the proposed scheme solutions are converging extremely faster comparable to different existing protocols.
Background: Turbulent flow is characterized by vortices with different scales. Extraction of various scales and filtering the turbulent field into coherent and incoherent parts are important processes that improve our understanding of turbulent characteristics. Objective: Joint probability distribution functions (JPDFs) for the filtered velocity gradient invariants are extensively studied for different scales as well as for the coherent and incoherent parts of each scale. Methods: The Fourier decomposition and the anisotropic diffusion model are used in the investigation. The extraction process is performed by employing the Fourier decomposition at different cutoff wavenumbers for the velocity field and three distinct scales (large, medium and fine scale) are identified. The velocity gradient invariants such as the second invariant Q and the third invariant R for the different scales are extracted. Then other important invariants such as the rate of rotation tensor QW and the rate of deformation QS are also identified for each scale. The anisotropic diffusion model is used to extract the coherent and incoherent parts of each invariant at each scale. Then the JPDFs of the coherent and incoherent invariants are compared. The scale decomposition and the filtering process are applied for turbulent flow fields that are simulated using the lattice Boltzmann method with resolution of 1283. Results: Results show that the (R-Q) space has a universal topological pear-like shape for the different scales as well as their coherent field. However, the (R-Q)-space for the incoherent fields are found different and no general shape can be observed. The (Qw-QS)-space results show self-similar shapes for coherent fields and for the incoherent fields no specific shape can be observed since the noise distributed as separated points everywhere. Conclusion: Two different methods for extraction and filtering of forced isotropic turbulence and the JPDFs of the velocity gradient invariants are studied. Some universal characteristics for the coherent parts were found. However, for the incoherent parts, no universal JPDFs were found.
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