A bounded upwinding scheme for computing convection-dominated transport problems

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data

Numerical Investigation Of Channel Flows With Emphasis On Coherent Structures And Turbulence Anisotropy

Numerical simulations of turbulent flows with pressure gradient effects are used to investigate the anisotropy of the Reynolds stress tensor near the wall and the presence of coherent structures. Incompressible, highly-resolved, Large Eddy Simulations (LES) are performed to investigate a convergent-divergent channel with a bump profile that induces a pressure gradient in the flow and a separation bubble. LES results are obtained using a semi-spectral formulation for low to moderate Reynolds numbers, ranging from Reτ = 180 to 950, based on the friction velocity at the channel inlet. The aim of this work is to analyse the effects of anisotropy along the channel using the Lumley triangle to evaluate the trajectories of the normalized Reynolds stress anisotropy tensor near the wall. This study is performed for different positions of the channel where favorable and adverse pressure gradients are present. Proper Orthogonal Decomposition (POD) is employed to isolate some coherent structures, reconstruct the flowfield and evaluate their effects in trajectories to isotropy. POD is also used to reconstruct the turbulent kinetic energy budget and to analyse the role of the large turbulent scales. © 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.46th AIAA Fluid Dynamics Conference, 201613 June 2016 through 17 June 201617593

Investigation Of Noise Sources In A Two-dimensional Model Airframe Noise Problem With Wake Interaction

Aeroacoustic predictions of a model airframe noise problem are conducted in order to assess the effects of wake and boundary layer interaction on both the flow and acoustic fields. Simulations of unsteady laminar ows, including both noise generation and its subsequent propagation to the far field, are performed for a two-dimensional configuration composed of a cylinder placed above a NACA 0012 airfoil at 5 deg. angle of incidence. The Reynolds number based on the airfoil chord is set at Rec = 5000 and the Reynolds number based on the diameter of the cylinder is Red = 200. An assessment of cylinder position and freestream Mach number effects on sound radiation is presented for M∞ = 0.1, 0.3 and 0.5. The investigation of the noise sources for airfoil and cylinder vortex shedding frequencies is also presented using a hybrid methodology which employs direct calculation for near field source computations and the Ffowcs Williams-Hawkings (FW-H) equation as the acoustic analogy formulation. In order to verify the numerical solutions, acoustic prediction results obtained by direct noise calculation (DNC) are compared to those computed by the FW-H equation and good agreement is observed. The separate contributions of the terms composing the quadrupole sources are analyzed. Even for the low Reynolds number flows investigated, Reynolds stresses are the dominant quadrupole noise sources and viscous effects as well as entropy fluctuations can be neglected. It is also found that while quadrupole sources can be neglected in noise predictions by the FW-H equation for the M∞ = 0.1 flow calculations, they should be included for the M∞ = 0.3 and 0.5 acoustic predictions at low and high frequencies. For moderate Mach number flows, at the cylinder vortex shedding frequency, dipole sources are related to both acoustic scattering and diffraction phenomena that occur along the airfoil surface and trailing edge, respectively. However, quadrupole sources are more specifically related to diffraction effects along the airfoil trailing edge. When the cylinder vortex shedding is the driving noise source mechanism, intense dipolar interference occurs for all configurations analyzed.118Numeca,Anecom Aerotest,MTU,Rolls-Royce,G.R.A.S. Sound and VibrationLighthill, M.J., On Sound Generated Aerodynamically I. General Theory (1952) Proceedings of the Royal Society A, 211, pp. 564-587Ffowcs Williams, J.E., Hawkings, D.L., Sound Generation by Turbulence and Surface in Arbitrary Motion (1969) Philosophical Transaction of the Royal Society of London, Series A, Mathematical and Physical Sciences, 264, pp. 321-342Wolf, W.R., Lele, S.K., Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems (2010) AIAA Journal, 48, pp. 2274-2285Wolf, W.R., Lele, S.K., Aeroacoustic Integrals Accelerated by Fast Multipole Method (2011) AIAA Journal, 49Casper, J.H., Lockard, D.P., Khorrami, M.R., Streett, C.L., Investigation of Volumetric Sources in Airframe Noise Simulations (2004) Proceedings of the 10th AIAA/CEAS Aeroacoustics Conference, pp. 1-10. , AIAA Paper 2004-2805Spalart, P.R., Shur, M.L., Strelets, M.K., Travin, A.K., Towards Noise Prediction for Rudimentary Landing Gear (2010) UTAM Symposium on Computational Aeroacoustics for Aircraft Noise PredictionWolf, W.R., Azevedo, J.L.F., Lele, S.K., Convective Effects and the Role of Quadrupole Sources for Aerofoil Aeroacoustics (2012) Journal of Fluid Mechanics, 708, pp. 502-538Wolf, W.R., Azevedo, J.L.F., Lele, S.K., Effects of Mean Flow Convection and Quadrupole Sources on Airfoil Trailing Edge Noise (2012) Proceedings of the 18th AIAA/CEAS Aeroacoustics Conference, pp. 1-19. , AIAA Paper 2012-2056Yu, C., Wolf, W.R., Lele, S.K., Quadrupole Noise in Turbulent Wake Interaction Problems (2012) Proceedings of the 18th AIAA/CEAS Aeroacoustics Conference, pp. 1-18. , AIAA Paper 2012-2057Nagarajan, S., Lele, S.K., Ferziger, J.H., A Robust High-Order Method for Large Eddy Simulation (2003) Journal of Computational Physics, 191, pp. 392-419Bhaskaran, R., Lele, S.K., Large Eddy Simulation of Free-stream Turbulence Effects on Heat Transfer to a High-pressure Turbine Cascade (2010) Journal of Turbulence, 11, pp. 1-15Lele, S.J., Compact Finite Difference Schemes with Spectral-Like Resolution (1992) Journal of Computational Physics, 103, pp. 16-42Beam, R.M., Warming, R.F., An Implicit Factored Scheme for the Compressible Navier-Stokes Equations (1978) AIAA Journal, 16, pp. 393-402Curle, N., The Inuence of Solid Boundaries Upon Aerodynamic Sound (1955) Proceedings of the Royal Society A, 231, pp. 505-514Ffowcs Williams, J.E., Hall, L.H., Aerodynamic Sound Generation by Turbulent Flow in the Vicinity of a Scattering Half Plane (1970) Journal of Fluid Mechanics, 40, pp. 657-67

Large Eddy Simulations Of Turbulent Flows With Adverse Pressure Gradients

The work presents comparative results between wall friction and pressure coefficient predictions from Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) computations in channel flows with an adverse pressure gradient created by a 2-D bump. Reynolds numbers range from Reτ = 617 to 2000, based on the friction velocity at the channel inlet. LES produces very consistent results when compared to DNS or other highly resolved LES. Twoequation and seven-equation RANS models are found to correctly predict friction coefficients in zero and favorable pressure gradient regions, but they fail in regions of adverse pressure gradients. The Reynolds stress transport model shows a better performance when compared to two-equation eddy-viscosity models, particularly in the higher Reynolds number cases. However, none of the RANS models is able to capture the full physics of turbulence related with adverse pressure gradients. Such limitations seem to be related to the fact that these models do not correctly describe the evolution of the turbulent kinetic energy close to the walls in adverse pressure gradient regions.Menter, F.R., Kuntz, M., Langtry, R., Ten years of industrial experience with the SST turbulence model (2003) Turbulence, Heat and Mass Transfer, 4. , Begell House, IncMarquillie, M., Laval, J.P., Dolganov, R., Direct numerical simulation of separated channel flows with a smooth profile (2008) Journal of Turbulence, 9 (1), pp. 1-23Marquillie, M., Ehrenstein, U., Laval, J.P., Instability of streaks in wall turbulence with adverse pressure gradient (2011) Journal of Fluid Mechanics, 681, pp. 205-240. , AugKuban, L., Laval, J.P., Elsner, W., Tyliszcak, A., Marquillie, M., LES modeling of converging-diverging turbulent channel flow (2012) Journal of Turbulence, 16 (11), pp. 1-19Jesus, A.B., Azevedo, J.L.F., Laval, J.P., Large eddy simulations and rans computations of adverse pressure gradient flows (2013) 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, , AIAA Paper No. AIAA 2013-0267, Grapevine, TX, JanJeyapaul, E., Rumsey, C., Analysis of highly-resolved simulations of 2-D humps toward improvement of second-moment closures (2013) 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, , AIAA Paper No. AIAA 2013-0684, Grapevine, TX, JanNicoud, F., Ducros, F., Subgrid-scale stress modelling based on the square of the velocity gradient tensor (1999) Flow, Turbulence and Combustion, 62, pp. 183-200(2011) ANSYS FLUENT Theory Guide, , ANSYS, Inc., Release 14.0, NovemberStanislas, M., Jimenez, J., Marusic, I., (2009) Progress in Wall Turbulence: Understanding and Modeling, , editors, ERCOFTAC. SpringerMarquillie, M., Ehrenstein, U., On the onset of nonlinear oscillations in a separating boundary-layer flow (2003) Journal of Fluid Mechanics, 490, pp. 169-188Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., (1988) Spectral Methods in Fluid Dynamics, , Springer-Verlarg, Berlin Heidelberg, 4th edKarniadakis, G.E., Israeli, M., Orszag, S.A., High-order splitting methods for the incompressible navier-stokes equations (1991) Journal of Computational Physics, 97, pp. 414-443Shih, T.H., Liou, W.W., Shabbir, A., Yang, Z., Zhu, J., A new k-e eddy-viscosity model for high reynolds number turbulent flows - model development and validation (1995) Computers and Fluids, 24 (3), pp. 227-238Launder, B.E., Shima, N., Second-moment closure for the near-wall sublayer: Development and application (1989) AIAA Journal, 27 (10), pp. 1319-1325Jesus, A.B., Schiavo, L.A.C.A., Azevedo, J.L.F., Laval, J.P., An assessment of attached and mildly separated flows in adverse pressure gradient regions (2014) 52nd AIAA Aerospace Sciences Meeting, , AIAA Paper No. AIAA 2014-0583, National Harbor, MD, Ja

Assessment Of Weno And Sfv High-order Reconstruction Schemes For Aerodynamic Flows

An assessment of two numerical formulations for high-order reconstruction on unstructured triangular grids is performed. TheWeighted Essentially Non-Oscillatory (WENO) and the Spectral Finite Volume (SFV) methods are considered for the spatial discretization of the 2-D Euler equations. Several test cases discussed in the literature are addressed here to assess the resolution properties, effective order of accuracy and performance of the spatial discretization schemes. The study compares, in particular, results for linear and quadratic reconstructions. The test cases include problems with strong shock waves and other discontinuities which provide a comparative assessment of the resolution capability of the tested schemes for typical aerospace flows. In order to perform such comparisons different limiter formulations are considered. One of such formulations include the use of both the WENO and SFV discretization methods for reconstruction, depending on the flow characteristics, to provide a continuous high-order solution field, regardless of discontinuities. It is hoped that the results of the present effort could provide valuable guidelines for future developments regarding high-order methods for unstructured meshes.American Institute of Aeronautics and Astronautics (AIAA)Wolf, W.R., Azevedo, J.L.F., High-Order Unstructured Essentially Non Oscillatory andWeighted Essentially Non Oscillatory Schemes for Aerodynamic Flows (2006) AIAA Journal, 44 (10), pp. 2295-2310. , OctWolf, W.R., Azevedo, J.L.F., High-Order ENO and WENO Schemes for Unstructured Grids (2007) International Journal for Numerical Methods in Fluids, 55 (10), pp. 917-943. , DecBreviglieri, C., Basso, E., Azevedo, J.L.F., (2008) High-Order Unstructured Spectral Finite Volume Scheme for Aerodynamic Applications, , AIAA Paper No. 2008-7182, 26th AIAA Applied Aerodynamics Conference, Honolulu, HI, AugBreviglieri, C., Azevedo, J.L.F., Basso, E., Souza, M.A.F., Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows (2010) AIAA Journal, 48 (10), pp. 2365-2376. , OctBreviglieri, C., Azevedo, J.L.F., (2012) Unsteady Aerodynamic Applications Using High-Order Unstructured Grid Methods, , AIAA Paper No. 2012-0701, 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Nashville, TN, JanWoodward, P., Colella, P., The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks (1984) Journal of Computational Physics, 54, pp. 115-173Roe, P.L., Approximatte Riemann Solvers, Parameter Vectors, and Difference Schemes (1981) Journal of Computational Physics, 43 (2), pp. 357-372Blazek, J., (2001) Computational Fluid Dynamics: Principles and Applications, , Elsevier, Oxford, UKSoetrisno, M., Imlay, S., Roberts, D., (1994) A Zonal Implicit Procedure for Hybrid Structured-Unstructured Grids, , AIAA Paper No. 94-0645Wang, Z.J., Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids: Basic Formulation (2002) Journal of Computational Physics, 178 (1), pp. 210-251. , MayWang, Z.J., Liu, Y., Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two-Dimensional Scalar Equation (2002) Journal of Computational Physics, 179 (2), pp. 665-698. , JulKnuth, D.E., (1998) The Art of Computer Programming, , 3: Sorting and Searching (2nd ed.), Addison-Wesley, Reading, MALiu, Y., Vinokur, M., Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids (1998) Journal of Computational Physics, 140 (1), pp. 122-147. , Febvan den Abeele, K., Lacor, C., An Accuracy and Stability Study of the 2D Spectral Volume Method (2007) Journal of Computational Physics, 226 (1), pp. 1007-1026. , SeptOllivier-Gooch, C., Quasi-ENO Schemes for Unstructured Meshes Based on Unlimited Data-Dependent Least-Squares Reconstruction (1997) Journal of Computational Physics, 133, pp. 6-17Friedrich, O., Weighted Essentially Non-Oscillatory Schemes for the Interpolation of Mean Values on Unstructured Grids (1998) Journal of Computational Physics, 144 (1), pp. 194-212. , JulyJiang, G.S., Shu, C.W., Efficient Implementation of Weighted ENO Schemes (1996) Journal of Computational Physics, 126 (1), pp. 77-99. , JuneAbgrall, R., On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation (1994) Journal of Computational Physics, 114, pp. 45-58Harten, A., Chakravarthy, S.R., (1991) Multi-Dimensional ENO Schemes for General Geometries, , ICASE Report 91-76Qiu, J., Shu, C.-W., A Comparison of Troubled-Cell Indicators for Runge-Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters (2006) SIAM J. Sci. Comput, 27 (3), pp. 995-1013Bigarella, E., (2007) Advanced Turbulence Modeling for Complex Aerospace Applications, , Ph. D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, BrazilMcDevitt, J., Okuno, A.F., (1985) Static and Dynamic Pressure Measurements on a NACA 0012 Airfoil in the Ames High Reynolds Number Facility, , NASA TP-2485, NASA, JunEmery, A., An Evaluation of Several Differencing Methods for Inviscid Fluid Flow Problems (1968) Journal of Computational Physics, 2, pp. 306-331Sonar, T., On the Construction of Essentially Non-Oscillatory Finite Volume Approximations to Hyperbolic Conservation Laws on General Triangulations: Polynomial Recovery, Accuracy and Stencil Selection (1997) Comput. Methods Appl. Mech. Engr, 140 (2), pp. 157-18

Dynamic Mode Decomposition Of High Reynolds Number Supersonic Jet Flows

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Current design constraints have encouraged the studies of aeroacoustic fields around compressible jet flows. The present work addresses the numerical study of unsteady turbulent jet flows as a preparation for future aeroacoustic analyses of main engine rocket plumes. An in-house large eddy simulation tool is used in order to reproduce high fidelity results of compressible jet flows. The large eddy simulation formulation is written using a second order numerical scheme for a finite difference spatial discretization. Numerical simulations of perfectly expanded jets are performed and the results are compared to the literature. Dynamic mode decompositions (DMD) of the jet flow, using large size three-dimensional snapshots, are performed. Three variables are analyzed, namely, the velocity magnitude, the vorticity magnitude and the divergence of velocity. In particular, two frequencies are identified and they are linked to flow structures observed in experiments performed by other authors in the literature. The spatial shapes of the corresponding dynamic modes are also discussed. © 2017 by S. Yamouni, C. Junqueira-Junior, J.L.F. Azevedo, and W.R. Wolf.150450/2016-8, CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico2013/07375-0, FAPESP, Fundação de Amparo à Pesquisa do Estado de São Paulo2013/21535-0, FAPESP, Fundação de Amparo à Pesquisa do Estado de São Paulo309985/2013-7, CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico400844/2014-1, CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico443839/2014-0, CNPq, Conselho Nacional de Desenvolvimento Científico e TecnológicoConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)55th AIAA Aerospace Sciences Meeting9 January 2017 through 13 January 201712642

A Comparative Study Of Discontinuous High Order Methods For Compressible Flows

A comparative study of three numerical formulations for discontinuous high-order reconstruction on unstructured grids is performed. TheWeighted Essentially Non-Oscillatory (WENO), the Spectral Finite Volume (SFV) and the Spectral Difference (SD) methods are considered for the spatial discretization of the 2-D Euler equations. The study compares, in particular, results for linear, quadratic and cubic reconstructions. The test cases include problems with strong shock waves and other discontinuities which provide a comparative assessment of the resolution capability of the tested schemes. This work explores the high-order method capabilities to solve literature test cases and it is expected that such results provide valuable guidelines for future developments regarding high-order methods for aerospace applications.Airbus,Boeing,Dunmore,et al,Georgia Innovation|Aerospace,Lockheed MartinMay, G., Iacono, F., Jameson, A., A Hybrid Multilevel Method for High-Order Discretization of the Euler Equations on Unstructured Meshes (2010) Journal of Computational Physics, 229 (10), pp. 3938-3956. , MayWang, Z.J., Fidkowski, K., Abgrall, R., Bassi, F., Caraeni, D., Cary, A., Deconinck, H., Visbal, M., High-Order CFD Methods: Current Status and Perspective (2013) International Journal For Numerical Methods In Fluids, 72 (8), pp. 811-845Roe, P.L., Approximatte Riemann Solvers, Parameter Vectors, and Difference Schemes (1981) Journal of Computational Physics, 43 (2), pp. 357-372Wang, Z.J., Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids: Basic Formulation (2002) Journal of Computational Physics, 178 (1), pp. 210-251. , MayWang, Z.J., Liu, Y., Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two-Dimensional Scalar Equation (2002) Journal of Computational Physics, 179 (2), pp. 665-698. , JulKnuth, D.E., (1998) The Art of Computer Programming. 3:Sorting and Searching, , 2nd ed.), Addison-Wesley, Reading, MALiu, Y., Vinokur, M., Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids (1998) Journal of Computational Physics, 140 (1), pp. 122-147. , Febvan den Abeele, K., Lacor, C., An Accuracy and Stability Study of the 2D Spectral Volume Method (2007) Journal of Computational Physics, 226 (1), pp. 1007-1026. , SeptOllivier-Gooch, C., Quasi-ENO Schemes for Unstructured Meshes Based on Unlimited Data-Dependent Least-Squares Reconstruction (1997) Journal of Computational Physics, 133, pp. 6-17Friedrich, O., Weighted Essentially Non-Oscillatory Schemes for the Interpolation of Mean Values on Unstructured Grids (1998) Journal of Computational Physics, 144 (1), pp. 194-212. , JulyWolf, W.R., Azevedo, J.L.F., High-Order Unstructured Essentially Nonoscillatory and Weighted Essentially Nonoscillatory Schemes for Aerodynamic Flows (2006) AIAA Journal, 44 (10), pp. 2295-2310. , OctJiang, G.S., Shu, C.W., Efficient Implementation of Weighted ENO Schemes (1996) Journal of Computational Physics, 126 (1), pp. 77-99. , JuneWolf, W.R., Azevedo, J.L.F., High-Order ENO and WENO Schemes for Unstructured Grids (2007) International Journal For Numerical Methods In Fluids, 55 (10), pp. 917-943. , DecAbgrall, R., On Essentially Non-Oscillatory Schemes on Unstructured Meshes: Analysis and Implementation (1994) Journal of Computational Physics, 114, pp. 45-58Harten, A., Chakravarthy, S.R., (1991) Multi-Dimensional ENO Schemes For General Geometries, , ICASE Report 91-76Qiu, J., Shu, C.-W., A Comparison of Troubled-Cell Indicators for Runge-Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters (2006) SIAM Journal On Scientific Computing, 27 (3), pp. 995-1013Bigarella, E., (2007) Advanced Turbulence Modeling For Complex Aerospace Applications, , Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, BrazilGeuzaine, C., Remacle, J.F., Gmsh: A Three-Dimensional Finite Element Mesh Generator with Built-in Pre- and Post-Processing Facilities (2009) International Journal For Numerical Methods In Engineering, 79 (11), pp. 1309-1331. , SepWang, Z.J., Liu, Y., May, G., Jameson, A., Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations (2007) Journal of Scientific Computing, 32 (1)May, G., Jameson, A., A Spectral Difference Method for the Euler and Navier-Stokes Equations on Unstructured Meshes (2006) AIAA Paper No. 2006-0304, 44th AIAA Aerospace Sciences Meeting, , Reno, NV, Janvan den Abeele, K., Lacor, C., Wang, Z.J., On the Stability and Accuracy of the Spectral Difference Method (2008) Journal of Scientific Computing, 37, pp. 162-188Spitieri, R.J., Ruuth, S.J., A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods (2003) SIAM Journal On Numerical Analysis, 40 (2), pp. 469-491Breviglieri, C., Paula, L.G.L., Wolf, W.R., Azevedo, J.L.F., Assessment of WENO and SFV High-Order Reconstruction Schemes for Aerodynamic Flows (2013) AIAA Paper No. 2013-2915, 31st AIAA Applied Aerodynamics Conference, , June, San Diego, CAShapiro, A.H., (1953) The Dynamics and Thermodynamics of Compressible Fluid Flow, , Wiley, New YorkBalan, A., May, G., Schöberl, J., A Stable High-Order Spectral Difference Method for Hyperbolic Conservation Laws on Triangular Elements (2012) Journal of Computational Physics, 231 (5), pp. 2359-2375. , MarMcDevitt, J., Okuno, A.F., (1985) Static and Dynamic Pressure Measurements On a NACA 0012 Airfoil In the Ames High Reynolds Number Facility, , NASA TP-2485, NASA, JunBreviglieri, C., Azevedo, J.L.F., Basso, E., Souza, M.A.F., Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows (2010) AIAA Journal, 48 (10), pp. 2365-2376. , OctYang, M., Wang, Z.J., A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids (2009) Advances In Applied Mathematics and Mechanics, 1 (4), pp. 451-480Emery, A., An Evaluation of Several Differencing Methods for Inviscid Fluid Flow Problems (1968) Journal of Computational Physics, 2, pp. 306-331Woodward, P., Colella, P., The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks (1984) Journal of Computational Physics, 54, pp. 115-173Sonar, T., On the Construction of Essentially Non-Oscillatory Finite Volume Approximations to Hyperbolic Conservation Laws on General Triangulations: Polynomial Recovery, Accuracy and Stencil Selection (1997) Computer Methods In Applied Mechanics and Engineering, 140 (2), pp. 157-181Breviglieri, C., Azevedo, J.L.F., Unsteady Aerodynamic Applications Using High-Order Unstructured Grid Methods (2012) AIAA Paper No. 2012-0701, 50th AIAA Aerospace Sciences Meeting, , Nashville, TN, JanCockburn, B., Shu, C.W., TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework (1989) Mathematics of Computation, 52. , 441-435Wang, Z.J., Liu, Y., Zhang, L., Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids IV: Extension to Two-Dimensional Systems (2004) Journal of Computational Physics, 194 (2), pp. 716-741. , Marc