Three-dimensional numerical simulation of flow around a 1:5 ... - IAWE

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Three-dimensional numerical simulation of flow around a 1:5 rectangular cylinder C. Mannini*, K. Weinman†, A. Šoda+, G. Schewe‡

*

CRIACIV/Department of Civil and Environmental Engineering, University of Florence, Italy [email protected] † Institute of Aerodynamics and Flow Technology, German Aerospace Center, Göttingen, Germany [email protected] + Faculty of Mechanical and Naval Engineering, University of Zagreb, Croatia [email protected] ‡

Institute of Aeroelasticity, German Aerospace Center, Göttingen, Germany [email protected]

Keywords: Computational Fluid Dynamics, Bluff bodies, Rectangular cylinder, Detached-Eddy Simulation, Turbulence modelling. ABSTRACT This paper deals with the three-dimensional simulation of the unsteady flow around a stationary 1:5 rectangular cylinder at zero-degree angle of attack, low Mach number and relatively high Reynolds number. The computations have been performed using the DLR-Tau code, a non-commercial finite-volume code developed at the German Aerospace Center, and results obtained with a hybrid mesh are validated against the available experimental data, showing good agreement. Detached-Eddy Simulation (DES), that is a hybrid method combining Large-Eddy Simulation (LES) and Raynolds-Averaged Navier-Stokes (RANS) approaches, has been adopted as strategy of turbulence modelling. The comparison with respect to unsteady RANS results, although obtained with advanced turbulence models, show the improvement that can be expected with the DES technique for this type of massively separated bluff-body flows. The paper also clarifies the key role played in LES, and therefore also in DES simulations, by the artificial dissipation characterizing the numerical scheme used to discretize the filtered Navier-Stokes equations. Finally, the discussed results highlight the effects of the spanwise extension of the computational domain. A distance between the periodic boundary planes equal to the width of the cylinder is not enough to allow the natural loss of correlation of pressures and the free development of large-scale turbulent structures. In contrast, a span equal to the double of the cylinder width fulfill much better this requirement. Contact person: C. Mannini, CRIACIV/Department of Civil and Environmental Engineering, University of Florence, Via S. Marta 3 – 50139 – Florence, Italy. Tel.: +39.055.4796326, FAX: +39.055.4796598 E-mail [email protected]

1. INTRODUCTION The simulation of unsteady separated flows around bluff bodies is still a challenging issue due to complex physical phenomena such as massive separation and reattachment, laminar-to-turbulent transition, alternating detachment of large eddies, interaction between large and small turbulent scales. In addition, the flow field is usually three-dimensional, even for simple two-dimensional geometries. The strategy of turbulence modelling is particularly important for the simulation of such flows. The employment of unsteady Reynolds-Averaged Navier-Stokes (URANS) equations represents a reasonable choice, given that two-dimensional geometries can be modelled with 2-D meshes and that the required grid and time resolutions are easily affordable. However, traditional turbulence model closures based on Boussinesq hypothesis are inaccurate for flows with significant boundary layer separation and strong streamline curvature as well as for three-dimensional flow. The URANS approach then shows limited accuracy. The alternative is to use Large-Eddy Simulation (LES) approach, which is expected to perform better for this type of flows. However, LES requires three-dimensional grids and wall-resolved LES (WRLES) becomes unaffordable when high-Reynolds-number thin turbulent boundary layers have to be resolved due to the necessary grid refinement (e.g. Spalart et al. 1997) as the costs are of the order of a poorly resolved Direct Numerical Simulation. Wall-modeled LES (WMLES) reduces computational requirements at high Reynolds numbers, but the decision as to the location of the interface between the LES and modeled flow regions is highly critical in the success of a zonal WMLES. In order to overcome this difficulty, which remains open, the non-zonal Detached-Eddy Simulation (DES) method has been introduced. DES is a hybrid RANS-LES technique that allows non-zonal switching between RANS and LES, so that RANS is employed in attached boundary layers and LES becomes active away from the boundary layer where significant turbulent kinetic energy can be economically resolved (i.e. restrictions on grid refinement are less severe away from attached boundary layer or free-shear layers). 3-D meshes are still needed and, while the number of grid points required for a properly designed DES mesh is not significantly higher than that for a URANS mesh, the requirement to resolve smaller time steps and the need to obtain statistical convergence for resolved fields have limited the use of DES within industry. Additionally, the notion of grid convergence within the LES community still remains to be properly resolved, particularly for unstructured solvers. In this paper a stationary two-dimensional rectangular cylinder with width-to-height ratio B/H = 5.0 at low Mach number (Ma = 0.1), relatively high Reynolds number (ReB = 132,000) and zero flow incidence (α = 0°) is considered. This is an interesting study case for the basic understanding of aerodynamics because the flow, which separates from the surface due to the sharp leading edges, reattaches on the side surfaces of the rectangular cylinder forming unsteady separation bubbles. In addition, the flow field is known to develop three-dimensional structures although the cylinder is two-dimensional. This geometry is considered to be a benchmark case for studies dealing with bridge aerodynamics and aeroelasticity (http://www.aniv-iawe.org/barc/; Païdoussis 2009). Therefore an experimental campaign on this profile conducted by one of the authors is underway in the High-Pressure Wind Tunnel of DLR-Göttingen (Schewe 2006, 2009). Numerical results obtained with the 3-D DES simulation are compared with experimental data, as well as with results of 3-D unsteady RANS approach. The role played by the extension of the computational domain in the spanwise direction is also investigated. Finally results of a computation with improved numerical algorithms, aimed mainly to reduce the numerical dissipation, are outlined. Two-dimensional URANS simulations for the same geometry at an angle of attack of 4° are discussed in Mannini et al. (2009), whilst results for an oscillating cylinder are reported in Mannini et al. (2007a).

2. NUMERICAL APPROACH 2.1

The DLR-Tau Code

Numerical simulations have been performed using the finite-volume unstructured solver DLR-Tau code (Gerhold et al. 1997, Schwamborn et al. 1999), developed by the German Aerospace Center (DLR). The code solves the compressible governing equations using vertex-centered metrics with second-order spatial and temporal accuracy. Inviscid fluxes are approximated using upwind, central and hybrid differencing schemes, while viscous terms are treated using a conventional second-order central differencing scheme. Either matrix or scalar dissipation can be used to stabilize the convective central difference operators. In the current work the Jameson-Schmidt-Turkel (JST) central differencing algorithm (Jameson et al. 1981) with scalar artificial dissipation is mainly adopted. Nevertheless, in a computation a modified version of JST central difference algorithm and matrix dissipation is also employed. For time-accurate calculations both dual and global time-stepping techniques are supported, along with multi-grid algorithms based on the agglomeration of the dual-grid volumes. In the dual-time-stepping approach the time derivatives are first discretized by a second-order backward difference formula and the resulting sequence of non-linear steady-state problems is solved in pseudo-physical time by an explicit Runge-Kutta or an implicit LU-SGS algorithm, until a steady state in pseudo-time is reached. In this work, where not differently specified, dual-time-stepping and explicit Runge-Kutta methods are used. The adequacy of the compressible Tau code to simulate low Mach number flows, was demonstrated in Haase et al. (2006). 2.2

Strategies of turbulence modelling

In the Reynolds-Averaged approach (RANS) the instantaneous quantities appearing in the Navier-Stokes equations are averaged over time. The ensemble averaging process results in additional unknown terms, the Reynolds stress tensor components, which have to be modeled. The turbulence closure considered in this work is the Linearised Explicit Algebraic Reynolds Stress Model, called LEA, proposed in Rung et al. (1999). LEA is applied to the basic k-ω two-equation turbulence model. Explicit Algebraic Reynolds Stress Models represent an alternative to the common linear Boussinesq relation, introducing the anisotropy tensor, which provides a more accurate representation of all components of the Reynolds stress tensor and allows to better capture rotation and curvature effects, without the drawbacks of high numerical effort and reduced robustness of a full differential-stress model. A more sophisticated method for the simulation of problems with massively separated flow is Detached-Eddy Simulation, a recent technique introduced in Spalart et al. (1997) and Shur et al. (1999). DES is a non-zonal hybrid RANS-LES method, and for the Spalart-Allmaras variant (SA-DES) used in this work the switching between the RANS and LES modes is controlled by the wall distance. This approach combines RANS model near solid walls where a WRLES type resolution of the flow is unaffordable or too expensive, and LES away from walls where massive separation occurs and a RANS formulation is not consistent with the flow physics. The switch between RANS and LES modus is based on a modified definition of the characteristic length scale d* in the Spalart-Allmaras (Spalart & Allmaras 1992) turbulence model, depending on the distance from the wall d and the largest edge length Δ of the local grid cell: d * = min {d , CDES Δ}

Δ = max {Δ x , Δ y , Δ z }

Near the wall d* = d, and therefore the RANS mode of the DES model is active. In regions where CDES Δ < d, d* = CDES Δ and, under an equilibrium assumption, the eddy-viscosity model reduces to a Smagorinsky sub-grid scale (SGS) model. The additional parameter with respect to pure URANS simulations is the constant CDES, and Shur et al. (1999) calibrate this parameter against decaying

homogeneous isotropic turbulence (DHIT) to ensure that the LES mode returns a proper turbulent kinetic energy cascade (i.e. the Kolmogorov 5/3’s law is resolved). CDES = 0.65 is the recommended value, obtained by adopting a centered fourth-order accurate differencing scheme. A smaller value of the DES constant can be used for more dissipative codes (e.g. Spalart 2001, Strelets 2001, Soda 2006). However, the optimal choice of CDES is closely tied into the numerical properties of the adopted numerical scheme. In this work, where not differently specified, CDES = 0.45 is assumed on the basis of calibration using DHIT in case of second-order accurate spatial discretization of the fluxes, as reported in Weinman et al. (2006). 2.3

Computational meshes

In this work a hybrid mesh is employed, that stems from the preliminary computations discussed in Mannini et al. (2007b). It is characterized by a structured-like node arrangement around the profile (body-aligned quadrilateral cells) and unstructured triangular cells in the remaining part of the domain. Figure 1 shows the 3-D grid (1,703,585 nodes and 2,957,440 cells) obtained by extruding a 2-D grid for one-chord length in the spanwise y-direction (S/B = 1.0), using 65 nodes to discretize the resulting edges (Δy/B = 0.0156). A grid with two-chord spanwise extension and same spacing (S/B = 2.0; Δy/B = 0.0156) has also been tested. The structured portion of the mesh consists of 28 layers with a stretching factor in the wall normal direction of 1.23, for a total height of 7.07e-02 B. The first structured layer height in the mesh is Δz1/B = 5.0e-05, chosen in order to have wall unit values in the normal direction z+ ≈ 1. Perfectly isotropic cells are obtained in the “focus region”, where the largest geometry-dependent turbulence structures are generated, which represents the optimal conformation for the LES mode of DES. With this grid and the value of the DES constant CDES = 0.45 the LES modus is active in the 86 % of the computational domain. Farfield boundary condition is assumed at one-hundred chord lengths away from the center of the prism, while viscous wall and periodic boundary conditions are imposed respectively at the body contour and at the lateral planes of the computational domain. The nondimensional time-step size is Δs = 0.0034, where s = tU∞/B is the number of traveled chord lengths in a time unit (U∞ = 34.0 m/s is the undisturbed flow speed), in order to discretize the expected period of vortex shedding with more than 500 time steps. This temporal discretization is finer than the one suggested by Spalart (2001) on the basis of the cell size in the focus region. 100 inner iterations are computed for each physical time step. 2.4

Simulations

In this work the results of four computations are presented. The first two simulations, that had already been discussed in details in Mannini et al. (2008), adopt the URANS approach combined with the LEA k-ω model and a basic version of DES, employing scalar dissipation (SD) to stabilize the convective central difference operators. Afterwards, in order to study the effect of spanwise extension of the computational domain, the same simulation has been repeated on a grid with S/B = 2.0 instead of S/B = 1.0. In order to improve the results and in particular to resolve smaller scales of turbulence in the cylinder wake, another computation is underway employing matrix instead of scalar artificial dissipation, along with a modified version of the JST central differencing algorithm based on Ducros sensor (Ducros et al. 1999, 2000), proposed by the second author of this paper. In fact, Figure 2 clearly shows that with both scalar and matrix dissipation, standard JST model and no preconditioning the simulation of the basic test case of DHIT is quite poor. Using scalar dissipation and low Mach-number preconditioning (Choi & Merkle 1993, Melber & Heinrich 2004) or modified JST model a significant improvement can be obtained but the simulation fails to reproduce the experimental spectrum at high wavenumber κ. Conversely the result is satisfactory with matrix dissipation and modified JST model both with and without preconditioning. This last simulation, that uses the computational mesh with S/B = 1.0, is also characterized by the Delayed DES approach (DDES), a modified version of DES proposed in order to avoid grid-induced

separation due to ambiguous grids (Spalart et al. 2006), although no significant difference are expected for this test case. In addition, the DES constant is set to 0.65, due to calibration with the less dissipative numerical scheme, and implicit backward-Euler time scheme is applied instead of explicit Runge-Kutta method. However, significant differences in the results are expected substantially for the use of matrix dissipation (MD) and modified JST scheme and therefore this computation is conventionally indicated in the following as MD.

Figure 1: Three-dimensional mesh used in the computations (S/B = 1.0).

Figure 2: Comparison against experiments of the spectrum of isotropic turbulence computed with several numerical approaches (κ is the wavenumber in m-1).

3. DISCUSSION OF RESULTS Results of the numerical simulations are reported in Table 1 in terms of Strouhal number (St), mean drag (CD) and lift (CL) coefficients and RMS-values of drag and lift coefficients (CDRMS and CLRMS). In the following, drag and Strouhal number are normalised with respect to the height H of the cylinder, while lift with respect to the width B. Experimental values obtained in the High-Pressure Wind Tunnel at DLR-Göttingen (Schewe 2006, 2009) are also reported. The measured drag is in perfect agreement with other wind-tunnel results available in literature (Nakamura & Mizota 1975, Mills et al. 2002, Matsumoto 2005), while for the Strouhal number the experimental data are more scattered: Nakamura & Yoshimura (1982) obtained St = 0.115, Okajima (Shimada & Ishihara 2002) St = 0.106, whereas Matsumoto et al. (2003) found a slightly larger value, i.e., St = 0.132. Comparison of the numerical results against experiments shows that the URANS-LEA simulation slightly underestimates the Strouhal number, whilst the lift mean fluctuation is significantly overpredicted. Non-negligible improvement can be obtained by applying DES, especially in terms of RMS-value of lift coefficient, which is reduced by almost 50 %. Nevertheless Strouhal number is still underestimated by about 7 %. By doubling the span extension of the computational domain no significant changes are observed for Strouhal number and mean drag, while the mean fluctuations of force coefficients, as expected, significantly go down and in particular CLRMS becomes even smaller than the reference experimental datum. Finally, the computation with matrix dissipation and modified JST scheme, although the signals are not long enough yet to calculate final statistics, shows a remarkable improvement in the Strouhal number value, which becomes very close to the experimental value. Also, an increase in the standard deviation of force coefficients can be observed. In the table the value of mean lift coefficient, which is obviously supposed to be zero, is reported as a rough indicator of statistical convergence of the computed time histories with respect to low frequency fluctuations. Figure 3 reports the evolution with time of computed lift and drag coefficient signals. It is evident that the result of the URANS-LEA simulation is nearly periodic, whereas significant chaotic behaviour characterises the other simulations due to the LES mode of DES. Figure 4 clearly shows the improvement obtained by using matrix dissipation and modified JST algorithm instead of basic scalar dissipation scheme in terms of power spectral density of the computed force coefficients.

3-D URANS-LEA (S/B = 1.0) 3-D SA-DES (S/B = 1.0) 3-D SA-DES (S/B = 2.0) 3-D SA-DES (MD – S/B = 1.0) Experiments (Schewe 2006, 2009)

St 0.095 0.103 0.103 0.111 0.111

CL 0.003 0.009 0.003 -0.007 0.0

CD 1.071 1.016 1.024 1.012 1.029

CLRMS 0.207 0.111 0.068 0.138 ~ 0.08

CDRMS 0.029 0.055 0.041 0.093

sINT 16.9 92.9 69.8 52.4

Table 1: Comparison between numerical and experimental results. St is the Strouhal number based on the cylinder height H, CD and CDRMS are respectively the mean and RMS values of drag coefficient, CL and CLRMS are the mean and RMS values of lift coefficient. Lift and drag coefficients are normalized respectively referring to the cylinder width B and height H. sINT is the number of convective time units over which the proposed integral results are calculated.

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Figure 3: Computed lift and drag coefficients. The dashed vertical lines indicate the convective time instants after which signals are considered in order to compute the variables reported in Table 1.

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Figure 4: Normalized power spectral density of lift and drag coefficients calculated on the same number of sample points for both simulations (sINT = 52.4). The dashed vertical lines denote the nondimensional dominant frequency of vortex shedding observed in the experiments (St = 0.111) and its double value (2St = 0.222).

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Figure 5: Vorticity magnitude (scaled with B/U∞) isocontours (14 levels from 7.5 to 40) relative to the midspan plane (y/B = 0.5).

The difference between results obtained with the basic DES simulation and with the one with matrix dissipation and modified JST scheme is even more evident if one looks at the instantaneous plots of the scaled vorticity contours proposed in Figure 5. It is worth noting that in the former case much finer turbulent structures are resolved and the potentiality offered by the computational grid and the chosen time-step size seems to be fully exploited. It is also clearly visible the shear-layer instability that gives rise to the unsteady wake. In contrast, with scalar dissipation the numerical dissipation is too high and damps out the high-wavenumber eddies, as expectable from the results of Figure 2. Obviously in the URANS-LEA simulation only the largest structures that characterize the mechanism of vortex shedding can be resolved. These results are confirmed by the instantaneous streamwise isovelocity surfaces shown in Figure 6. Once again much finer and complex structures can be observed in the flow field computed with DES and matrix dissipation. It is also worth noting that the flow field computed with the URANS-LEA approach is almost two-dimensional, thus making practically useless the much increased computational effort due to the use of a three-dimensional mesh (Mannini et al. 2008). In Figure 7 the computed mean and RMS-values of pressure coefficient distribution on the body contour are compared with wind-tunnel data. Numerical results are overall in good agreement with experiments, although significant scatter affects the RMS values of the wind-tunnel results. The DES simulation with matrix dissipation predicts much larger fluctuations of pressures on the rear face of the cylinder, closer to experimental evidences. The large values of experimental Cp’ on the front side of the cylinder are probably due to oncoming wind-tunnel turbulence. By the analysis of streamwise distribution of time-averaged skin friction (not reported here for the sake of brevity), it is possible to conclude that all the computations predict approximately the same position for the time-averaged reattachment of flow on the lateral faces of the cylinder, located at x/B

≈ 0.43 (x = 0 denotes the centre of the rectangular cylinder). Despite that, the skin friction calculated with matrix dissipation presents a very different pattern as compared to the other results. This is due to different mean flow field near the leading edge, where the counter-rotating vortex embedded in the main separation bubble, obtained with the DES computation with scalar dissipation, is no longer present (Figure 8). As a consequence, also the position of the center of the time-averaged bubble slightly migrates downstream. In contrast, no significant difference in the length of the mean recirculation region behind the body can be observed: the saddle point is located at x/B ≈ 0.65 for the DES computation with matrix dissipation and at x/B ≈ 0.68 for that with scalar dissipation.

Figure 6: Snapshots of streamwise isovelocity surfaces (Vx = 0). Air flows from the right to the left. 3-D URANS-LEA (S/B = 1.0) 3-D SA-DES - SD (S/B = 1.0) 3-D SA-DES - SD (S/B = 2.0) 3-D SA-DES - MD (S/B = 1.0)

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Figure 7: Comparison with experiments of the computed mean (left) and RMS-values (right) of the pressure coefficient distribution at midspan (y/B = 0.5). ξ/B = 0 and ξ/B = 1.2 denote respectively the impingement and the base body contour points. Wind-tunnel results Exp. [1] are taken from Schewe (2006, 2009), Exp. [2] from Matsumoto (2005), Exp. [3] from Galli (2005) and Exp. [4] from Ricciardelli & Marra (2008).

Figure 8: Streamlines of time-averaged flow field at spanwise position y/B = 0.5.

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Figure 9: Coefficient of correlation in the spanwise direction of the surface pressures relative to the positions x/B = ±0.32 (x = 0 denotes the midchord position). ry is the spanwise separation.

Finally Figure 9 shows the spanwise correlation of pressures obtained with different computations and compared with experimental results (Ricciardelli & Marra 2008) at two streamwise positions. As expected, the higher correlation is obtained with the URANS simulation, where a nearly 2-D flow field is computed. As for DES, one can observe a decay of correlation with the spanwise separation ry but the periodic boundary condition imposed at the lateral plane artificially increase the coherence of fluctuations. This is particularly effective when the distance between the periodic planes is limited to one time the cylinder width (S/B = 1.0), as pressures are not free to naturally de-correlate. In terms of integral quantities, this implies higher values of mean fluctuations of force coefficients. In contrast, a double spanwise extension of the computational domain (S/B = 2.0), seems to allow a free de-correlation of fluctuating quantities, although the correlation still artificially increases when approaching the second periodic plane. In this case, it can be observed that at the downstream position (x/B = 0.32), near the time-averaged reattachment point, the agreement found with the experimental data is excellent. Conversely, near the leading edge (x/B = -0.32) pressures de-correlate much faster than in the experiments and after a spanwise separation ry = 0.4B the fluctuations are already uncorrelated. This disagreement with experiments, which is hidden in the computation with S/B = 1.0, may be due to an incorrect development of separation near the leading edge. On this point, it is worth reminding that the counter-rotating vortex embedded in the time-averaged separation bubble is no longer present if the flow field is simulated with matrix dissipation and modified JST scheme (Figure 8).

4. CONCLUSIONS The flow around a 1:5 rectangular cylinder at zero-degree angle of attack has been simulated with different approaches and reasonable to good agreement is obtained with experimental data. The paper shows the improvement in the accuracy of results and in the simulated flow physics that can be expected by the use of DES instead of URANS method, even if the latter is combined with advanced and well performing turbulence models. Moreover, the comparison between computations performed on the same grid with different spanwise extension clearly shows the key role played by this parameter. As a matter of fact, if the spanwise extension S of the computational domain is too small (for instance S = B = 5H), the periodic boundary conditions imposed at the lateral planes do not allow the natural de-correlation in that direction of quantities such surface pressures. As a result, the formation of low-wavenumber eddies is influenced by this restriction and larger mean fluctuations of integral quantities, such as lift and drag coefficients, are obtained. A span equal to two times the cylinder width (S = 2B = 10H) allows much better the expected de-correlation of the flow field. Finally, the paper highlights the importance for a LES or DES simulation to keep low the artificial dissipation due to the numerical discretization schemes. In fact, this dissipation is able to damp out all the high-wavenumber eddies that could be resolved with fine enough grid and time-step size. Results show that the loss of physical interaction between small and large scale turbulence can have a significant effect on the mean flow field and on the large-scale mechanism of vortex shedding, reducing also the accuracy in the prediction of integral quantities of practical engineering interest. ACKNOWLEDGEMENT This work has been performed in the framework of the DLR projects (2007-2008) “Numerische Simulation der Umströmung stumpfer Körper” and “3D-Effekte bei abgelösten Strömungen” (2009-2011). The received support is gratefully acknowledged. Dr. Ralph Voβ and Dr. Tobias Knopp, respectively from the Institute of Aeroelasticity and from the Institute of Aerodynamics and Flow Technology of DLR Göttingen, are also thanked for their suggestions and the helpful discussions. The help of Urte Fürst in using the computer cluster of the DLR Institute of Aeroelasticity is also gratefully acknowledged. Finally the authors would like to thank Prof. Masaru Matsumoto, from the University of Kyoto, Japan, for the experimental data he kindly made available. REFERENCES Choi Y.-H., Merkle C.L. (1993). “The application of preconditioning in viscous flows”, Journal of Computational Physics, 105 (2), 207-223. Ducros F., Ferrand V., Nicoud F., Weber C., Darracq D., Gacherieu C. and Poinsot T. (1999). “Large-Eddy Simulation of the shock/turbulence interaction”, Journal of Computational Physics, 152 (2), 517-549. Ducros F., Laporte F., Soulères T., Guinot V., Moinat P. and Caruelle B. (2000). “High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows”, Journal of Computational Physics, 161 (1), 114-139. Galli F. (2005). Comportamento aerodinamico di strutture snelle non profilate: approccio sperimentale e computazionale. Master’s thesis, Politecnico di Torino, Turin, Italy. Gerhold T., Galle M., Friedrich O., Evans J. (1997). “Calculation of complex three-dimensional configurations employing the DLR-Tau code”. In Proceedings of the 35th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 97-0167, Reno, Nevada. Haase W., Aupoix B., Bunge U., Schwamborn D. (2006). “Flomania - a European Initiative on Flow Physics Modelling”. In Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 94, Springer, Berlin Heidelberg New York. Hansen R.P., Forsythe J.R. (2003). “Large and Detached Eddy Simulations of a circular cylinder using unstructured grids”. In Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2003-0775, Reno, Nevada. Jameson A., Schmidt W., Turkel E. (1981). “Numerical solutions of the Euler equations by finite volume methods using

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