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Numerical assessment of stratification influence in simple algebraic turbulence model
Uhlíř, V. ; Bodnár, Tomáš ; Caggio, Matteo
This paper presents rst few results obtained using a newly developed test code aimed at validation and cross-comparison of turbulence models to be applied in environmental flows. A simple code based on nite di erence discretization is constructed to solve steady flows of incompresible non-homogeneous (variable denstity) fluids. For the rst tests a simple algebraic turbulence model was implemented, containing stability function depending on the stratification via the gradient Richardson number. Numerical tests were performed in order to explore the capabilities of the new code and to get some insight into its behavior under di erent stratification. The two-dimensional simulations were performed using immersed boundary method for the flow over low smooth hill. The resulting flow fields are compared for selected Richarson numbers ranging from stable up to unstable strati cation conditions.
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Numerical tests of vanishing diffusion stabilization in Oldroyd-B fluid flow simulations
Pires, M. ; Bodnár, Tomáš
This work presents some numerical tests of finite element solution of incompressible Oldroyd-B fluids flows, using different types of numerical stabilization. In this study the diffusive term (Laplacian of extra stress) is added to the tensorial constitutive relation where it is multiplied by a coefficient, that is variable in time. The goal is to make this diffusion coefficient vanish in time, so that the final solution remains unaffected by the added diffusion term. A series of numerical tests was performed for the steady two-dimensional Oldroyd-B fluid flow in corrugated channel (tube) to compare different versions of the vanishing stabilization terms and assess their efficiency in enforcing the solution convergence, without affecting the final steady state.
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Second-order model for atmospheric turbulence without critical Richardson number
Caggio, M. ; Schiavon, M. ; Tampieri, F. ; Bodnár, Tomáš
The purpose of this communication is to present a derivation of the non-dimensional vertical gradients of the mean wind speed and mean potential temperature expressed in terms of the so-called similarity functions for very stable conditions of the atmosphere where theoretical approaches provide conflicting results (see e.g. Luhar et al. [19]). The result is based on the analysis of the second-order model equations in the boundary layer approximations in which new heat flux equations are proposed. The model employs a recent closure for the pressure-temperature correlation, avoiding the issue of a critical treshold for the Richardson number.
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On the influence of diffusion stabilization in Oldroyd-B fluid flow simulations
Pires, M. ; Bodnár, Tomáš
This work presents some numerical tests of finite element solution of incompressible Oldroyd-B fluid flows. The effect of numerical stabilization using artificial stress diffusion is investigated in detail. The limits of Weissenberg number We for which it is possible to obtain the numerical solution were studied depending on the Reynolds number Re and the diffusion parameter. Series of numerical tests were performed for steady two-dimensional Oldroyd-B fluid flow in corrugated channel (tube). The numerical results clearly proved the advantage (higher attainable We) of stabilized numerical method over the classical formulation without the artificial stress diffusion.
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Recent results on the problem of motion of viscous fluid around a rotating rigid body
Deuring, P. ; Kračmar, Stanislav ; Nečasová, Šárka
We consider the linearized incompressible flow around rotating and translating body in the exterior domain R³D‾, where D⊂R³ is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure. Further, we consider the linearized problem in a truncation domain DR:=BRD‾ of the exterior domain R³D‾ under certain artificial boundary conditions on the truncating boundary ∂BR, and then compare this solution with the solution in the exterior domain R³D‾ to get the truncation error estimate.
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