Turbulent Channel Flow With a Modified k-ω Turbulence Model for High-Order Finite Element Methods

Abstract One-dimensional fully developed channel flow was solved using a modified k–ω turbulence model that was recently proposed for use with high-order finite element schemes. In order to study this new turbulence model’s behavior, determine its dependence on boundary conditions and model constants, and find efficient methods for obtaining solutions, the model was first examined using a linear finite element discretization in 1D. The results showed that an accurate estimate of the parameter εk which is used to define k in terms of the working variable k~ is essential to get an accurate solution. Also, the turbulence model depended sensitively on an accurate estimate of the distance of the first grid point from the wall, which can be difficult to estimate in unstructured grids. This is used for the boundary condition of specific dissipation rate on the wall. This model was then implemented in a high-order finite element code that uses an unstructured mesh of triangles to verify that the 1D results were predictive of the behavior of the full 2D discretization. High-order 2D results were obtained on triangular meshes with element aspect ratios up to 250000.

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214 Turbulent channel flow Analysis of Finite Element Methods with High-Order Element

The Proceedings of Conference of Kansai Branch ◽

10.1299/jsmekansai.2006.81._2-20_ ◽

2006 ◽

Vol 2006.81 (0) ◽

pp. _2-20_

Author(s):

Shinichiro MIURA

Keyword(s):

Finite Element ◽

Channel Flow ◽

Finite Element Methods ◽

Flow Analysis ◽

Turbulent Channel Flow ◽

High Order ◽

High Order Element ◽

Order Element

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Order of Accuracy and Sensitivity to Freestream Conditions of a Modified k-ω Turbulence Model for High-Order Finite Element Methods

Volume 3: Computational Fluid Dynamics; Micro and Nano Fluid Dynamics ◽

10.1115/fedsm2020-20297 ◽

2020 ◽

Author(s):

Nojan Bagheri-Sadeghi ◽

Brian T. Helenbrook ◽

Kenneth D. Visser

Keyword(s):

Boundary Condition ◽

Finite Element ◽

Flat Plate ◽

Turbulence Model ◽

Finite Element Methods ◽

Incompressible Flows ◽

Grid Point ◽

High Order ◽

Surface Boundary ◽

Wall Distance

Abstract Using turbulence models with finite element methods (FEM) can be challenging as the turbulence variables can assume negative non-physical values and hinder solution convergence. A modified k–ω model was recently proposed by Stefanski et al. (2018) to be used with finite element solvers of compressible flows. The model overcomes this issue by replacing k and ω with working variables that ensure positivity and smoothness of k and ω. In this work the applicability of this model for high-order FEM simulations of incompressible flows was examined. The model was implemented for incompressible flow in an hp-FEM solver using streamline Petrov-Galerkin discretization and was validated and verified using a fully-developed channel flow and a boundary layer flow over a flat plate. Several aspects of the turbulence model behavior were studied. These included the possibilitty of getting orders of accuracy higher than 2, and the model’s sensitivity to freestream values of k and ω. The results suggested that higher orders of accuracy are possible when quadratic and quartic basis functions are used. However, this depended on the way the boundary condition for ω was defined. The commonly used boundary condition for ω, which depends on the wall-distance of the first grid point resulted in poor orders of accuracy compared to the so-called slightly-rough-surface boundary condition which is independent of the wall distance of the first grid point. Additionally, results indicated that increasing the nondimensional wall distance of the first gridpoint makes it more sensitive to the value of ω on the wall. Adding a cross-diffusion term to the transport equation for ω is known to significantly improve the accuracy of turbulence model prediction for certain flows and reduce the sensitivity of the original k–ω model to freestream values of turbulence variables. Following a more recent version of k–ω model, this term was added to the turbulence model and some other modifications including a different production term with a stress-limiter were applied. The drag coefficient of the flat plate from the new turbulence model showed similar sensitivity to the freestream values of turbulence variables as the model of Stefanski et al. (2018).

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Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202514400028 ◽

2014 ◽

Vol 24 (08) ◽

pp. 1495-1539 ◽

Cited By ~ 22

Author(s):

Francesco Bassi ◽

Lorenzo Botti ◽

Alessandro Colombo

Keyword(s):

Finite Element ◽

Convergence Rates ◽

Numerical Test ◽

High Order ◽

Test Cases ◽

Computational Domain ◽

Element Discretization ◽

Mesh Free ◽

Domain Boundaries ◽

Coarse Grids

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

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A Multi-Field Space-Time Finite Element Method for Structural Acoustics

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0395 ◽

1995 ◽

Author(s):

Lonny L. Thompson

Keyword(s):

Finite Element ◽

Time Domain ◽

Acoustic Waves ◽

Space Time ◽

High Order ◽

Elastic Structure ◽

Structural Acoustics ◽

Field Representation ◽

Element Discretization ◽

Acoustic Fluid

Abstract A Computational Structural Acoustics (CSA) capability for solving scattering, radiation, and other problems related to the acoustics of submerged structures has been developed by employing some of the recent algorithmic trends in Computational Fluid Dynamics (CFD), namely time-discontinuous Galerkin Least-Squares finite element methods. Traditional computational methods toward simulation of acoustic radiation and scattering from submerged elastic bodies have been primarily based on frequency domain formulations. These classical time-harmonic approaches (including boundary element, finite element, and finite difference methods) have been successful for problems involving a limited range of frequencies (narrow band response) and scales (wavelengths) that are large compared to the characteristic dimensions of the elastic structure. Attempts at solving large-scale structural acoustic systems with dimensions that are much larger than the operating wavelengths and which are complex, consisting of many different components with different scales and broadband frequencies, has revealed limitations of many of the classical methods. As a result, there has been renewed interest in new innovative approaches, including time-domain approaches. This paper describes recent advances in the development of a new class of high-order accurate and unconditionally stable space-time methods for structural acoustics which employ finite element discretization of the time domain as well as the usual discretization of the spatial domain. The formulation is based on a space-time variational equation for both the acoustic fluid and elastic structure together with their interaction. Topics to be discussed include the development and implementation of higher-order accurate non-reflecting boundary conditions based on the exact impedance relation through the. Dirichlet-to-Neumann (DtN) map, and a multi-field representation for the acoustic fluid based on independent pressure and velocity potential variables. Numerical examples involving radiation and scattering of acoustic waves are presented to illustrate the high-order accuracy achieved by the new methodology for CSA.

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