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

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

Efeito do óleo essencial de pimenta longa (Piper hispidinervum C. DC) e do emulsificante Tween® 80 sobre o crescimento micelial de Alternaria alternata (Fungi: Hyphomycetes) The effect of Long-pepper essential oil (Piper hispidinervum C. DC.) and of Tween®; 80 emulsifier on the mycelial growth of Alternaria alternate (Fungi: Hyphomycetes)

Este trabalho objetivou avaliar o efeito do óleo essencial de folhas de pimenta longa (Piper hispidinervum C. DC), sobre o crescimento micelial de Alternaria alternata e a análise da influência da concentração do emulsificante Tween® 80 no controle deste fitopatógeno. O óleo essencial foi obtido pela técnica "arraste a vapor d'água", utilizando-se aparelho de Clevenger modificado, e posteriormente submetido, à análise por cromatografia em fase gasosa acoplada a espectrômetro de massas CG-EM a CG. Para os ensaios biológicos, o método foi o bioanalítico in vitro observando-se o crescimento ou inibição do micélio de A. alternata no meio de cultura BDA na presença de diferentes concentrações do óleo essencial (0, 100, 250, 500 e 1000 mgL-1 ) sob diferentes concentrações de Tween® 80. Adotou-se esquema fatorial com quatro repetições, em delineamento inteiramente casualizado (DIC). Observou-se que o óleo essencial de pimenta longa apresentou inibição sobre o crescimento micelial do fungo A. alternataem todas as concentrações analisadas, sendo que na concentração de 1000 mgL-1 esta inibição foi de 100% , e a porcentagem de emulsificante (Tween® 80), influenciou na atividade fungitóxica das concentrações de 250 mgL -1 e 500 mgL -1 do óleo essencial.<br>The object of this work was to evaluate the effectof essential oils from Long-pepper leaves Piper hispidinervum on the mycelial growth of Alternaria alternata and to analyze the influence of emulsifier Tween® 80 concentration in the control of this phytopathogen. The essential oil was obtained by steam stream distillation, using a modified Clevenger apparatus, and the chemical composition was analyzed by gas chromatography coupled to mass spectroscopy GC-MS and GC. For biological tests, the bioanalytical in vitro method was used, observing the growth or inhibition of such phytopathogen in BDA culture media, in the presence of different essential oil concentrations (0, 100, 250, 500, e 1000 mgL -1) under different Tween® 80 concentrations. Factorial scheme with four repetitions, in entirely randomized outline was adopted. The essential oil of Long-pepper inhibited the micellial growth of the A. alternata fungus at all of the concentrations tested. A 100% inhibition at the 1000 mgL -1 concentration was observed, and the percentage of emulsifier (Tween® 80) influenced the fungitoxic activity at the 250 mgL-1 and 500 mgL -1 concentrations of the essential oil