scholarly journals On the use of a cell-centered finite-volume scheme on prismatic meshes in boundary layers

2021 ◽  
pp. 1-44
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Reynolds Number ◽  
Finite Volume ◽  
High Reynolds Number ◽  
Finite Volume Scheme ◽  
Wall Surface ◽  
One Dimensional ◽  
Volume Scheme ◽  
Dimensional Reconstruction ◽  
A Cell ◽  
High Reynolds

We consider the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction and generalize it to anisotropic prismatic meshes suitable for high-Reynolds-number problems. We offer a new algorithm of flux computation based on the reconstruction along the wall surface, whereas in the original schemes it was along the tangent to the wall surface. We also study how does the curvature of mesh elements influence the accuracy if taken into account.

Models of the scalar spectrum for turbulent advection

1978 ◽  
Vol 88 (3) ◽  
pp. 541-562 ◽  
Author(s):  
R. J. Hill
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Temperature Fluctuations ◽  
Limited Extent ◽  
Temperature Spectrum ◽  
One Dimensional ◽  
Moderate Reynolds Number ◽  
Temperature Spectra ◽  
High Reynolds

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

scholarly journals Accuracy analysis and improvement for the cell-centered scheme with the quasi-one-dimensional reconstriction

2021 ◽  
pp. 1-32 ◽  
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Transport Equation ◽  
Finite Volume ◽  
Constant Velocity ◽  
Truncation Error ◽  
Finite Volume Scheme ◽  
Accuracy Analysis ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Reconstruction

We study the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction. For the model transport equation with a constant velocity, we prove that on translationally-invariant (TI) triangular meshes it possesses the second order of the truncation error and, if the solution is steady, the third order of the solution error. We offer the modification possessing the third order of the solution error on TI-meshes for unsteady solutions also and verify its accuracy on unstructured meshes.

Development of a New Algorithm for Modeling Viscous Transonic Flow on Unstructured Grids at High Reynolds Numbers

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Rozie Zangeneh
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Flows ◽  
Transonic Flow ◽  
High Reynolds Number ◽  
Unstructured Grids ◽  
Separation Bubble ◽  
Aircraft Design ◽  
Finite Volume Scheme ◽  
High Reynolds

Abstract This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

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