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Conservative Residual Distribution Method for Viscous Double Cone Flows in Thermochemical Nonequilibrium

  • Andrea Lani (a1), Marco Panesi (a2) and Herman Deconinck (a1)


A multi-dimensionally upwind conservative Residual Distribution algorithm for simulating viscous axisymmetric hypersonic flows in thermo-chemical nonequilibrium on unstructured grids is presented and validated in the case of the complex flow-field over a double cone configuration. The resulting numerical discretization combines a state-of-the-art nonlinear quasi-monotone second order blended scheme for distributing the convective residual and a standard Galerkin formulation for the diffusive residual. The physical source terms are upwinded together with the convective fluxes. Numerical results show an excellent agreement with experimental measurements and available literature.


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[1]Barbante, P. F., Degrez, G., and Sarma, G. S. R., Computation of Nonequilibrium High-Temperature Axisymmetric Boundary-Layer Flows, J. Thermophys. Heat Transfer, Vol. 16 (2002), No. 4, pp. 490497.
[2]Bottin, B., Vanden Abeele, D., Carbonaro, M., Degrez, G., and Sarma, G. S. R., Thermodynamic and Transport Properties for Inductive Plasma Modeling, J. Thermophys. Heat Transfer, Vol. 13(1999), pp. 343350.
[3]Candler, G. V. and MacCormack, , Computation of Weakly Ionized Hypersonic Flows in Ther-mochemical Nonequilibrium, J. Thermophys. Heat Transfer, Vol. 5, No. 11 (1991), pp. 266273.
[4]Ćsik, Á., Upwind Residual Distribution Schemes for General Hyperbolic Conservation Laws and Application to Ideal Magnetohydrodynamics, Ph.D. thesis, Katholieke Universiteit Leuven, Faculteit Wetenschappen Centrum voor Plasma-Astrofysica, Belgium, 2002.
[5]Ćsik, Á, Ricchiuto, M., Deconinck, H., A conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws, J. Comput. Phys., Vol. 179, No. 2(2002), pp. 286312.
[6]Deconinck, H., Ricchiuto, M., Sermeus, K., Introduction to residual distribution schemes and stabilized finite elements, VKI LS 2003-05, 33rdComputational Fluid Dynamics Course, von Karman Institute for Fluid Dynamics, 2003.
[7]Deconinck, H., Roe, P. L., Struijs, R., A multidimensional generalization of Roe’s difference splitter for the Euler equations, Computer and Fluids, Vol. 22, No. 2/3 (1993), pp. 215222.
[8]Degrez, G., van der Weide, E., Upwind residual distribution schemes for chemical nonequilibrium flows, Paper 99-3366, 14th AIAA Computational Fluid Dynamics Conference, Norfolk, USA, June 28-July 1, 1999.
[9]Dobeš, J., Numerical Algorithms for the Computation of Unsteady Compressible Flows over Moving Geometries. Applications to Fluid-Structure Interaction, PhD thesis submitted at Czech Technical University, Prague, Czech Republic, University Libre de Bruxelles, Belgium, November 2007.
[10]Dobeš, J. and Deconinck, H., A Shock Sensor-Based Second-Order Blended (Bx) Upwind Residual Distribution Scheme for Steady and Unsteady Compressible Flow, in Hyperbolic Problems: Theory, Numerics, Applications, 978-3-540-75711-5 (print), 978-3-540-75712-2 (online), pp. 465473, 2008, Springer Berlin Heidelberg.
[11]Gnoffo, P. A., Gupta, R. N., and Shinn, J. L., Conservation equations and physical models for hypersonic air flows in thermal and chemical non-equilibrium. Technical Paper 2867, NASA, 1989.
[12]Gupta, R. N., Yos, J. M., Thompson, R. A., and Lee, K. P., A review of reaction rates and ther-modynamic and transport properties for an 11-species air model for chemical and thermal non-equilibrium calculations to 30 000 K. Reference Publication 1232, NASA, August 1990.
[13]Hirschfelder, J. O., Curtiss, C. F. and Bird, R. B., Molecular theory of gases and liquids, Wiley, New York, 1954.
[14]Issmann, E., Degrez, G., Deconinck, H., Implicit upwind residual distribution Euler and Navier-Stokes solver on unstructured meshes, AIAA Journal, Vol. 34(1996), pp. 20212028.
[15]Knight, D., Longo, J., Drikakis, D., Gaitonde, D., Lani, A., Nompelis, I., Reimann, B. and Walpot, L., Assessment of CFD Capability for Prediction of Hypersonic Shock Interactions, Prog. Aerospace Sci., to appear.
[16]Lani, A., Quintino, T., Kimpe, D., Deconinck, H., Vandewalle, S., Poedts, S., The COOLFluiD Framework: Design Solutions for High-Performance Object Oriented Scientific Computing Software, Computational Science – ICCS 2005, LNCS 3514, Springer-Verlag, Vol. 1(2005), pp. 281286.
[17]Lani, A., Quintino, T., Kimpe, D., Deconinck, H., Vandewalle, S., Poedts, S., Reusable Object-Oriented Solutions for Numerical Simulation of PDEs in a High Performance Environment, Scientific Programming, ISSN 1058-9244, IOS Press, Vol. 14, No. 2 (2006), pp. 111139.
[18]MacLean, M., Holden, M., Wadhams, T. and Parker, R., A computational analysis of thermochemical studies in the lens facilities. ph45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (US), AIAA 207-121, Jan 2007.
[19]Magin, T. E., Degrez, G., Transport algorithms for partially ionized unmagnetized plasmas, J. Comput. Phys., Vol. 198(2004), pp. 424449.
[20]Magin, T. E., Degrez, G., Transport properties for partially ionized unmagnetized plasmas, Phys. Rev. E, Vol. 70(2004).
[21]Millikan, R. C. and White, D. R., Systematics of vibrational relaxation. J. of Chem. Phys., Vol. 39, No. 12(1963), pp. 32093213.
[22]Nishikawa, H., A First-Order System Approach for Diffusion Equation. I: Second-Order Residual Distribution Schemes, J. Comput. Phys., 227 (2007), pp. 315352.
[23]Nishikawa, H., A First-Order System Approach for Diffusion Equation. II: Unification of Advection and Diffusion, J. Comput. Phys., 229 (2010), pp. 39894016.
[24]Nishikawa, H., New-Generation Hyperbolic Navier-Stokes Schemes: (1/h) Speed-Up and Accurate Viscous/Heat Fluxes, AIAA Paper 2011-3043, 20th Computational Fluid Dynamics Conference, June 2011.
[25]Nompelis, I., Drayna, T. W and Candler, G. V., A Parallel Implicit Solver for Hypersonic Reacting Flow Simulation, AIAA 2005-4867, 17th AIAA Computational Fluid Dynamics Conference, Toronto, Canada, June 6-9, 2005.
[26]Nompelis, I., Computational Study of Hypersonic Double-Cone Experiments for Code Validation, PhD Thesis, University of Minnesota, May 2004.
[27]Paillere, H., phMulti-dimensional Upwind Residual Distribution Schemes for the Euler and Navier-Stokes Equations on Unstructured Grids. PhD thesis, Universite Libre de Bruxelles, 1995.
[28]Park, C., Nonequilibrium Hypersonic Aerothermodynamics, John Wiley and Sons, New York, 1989.
[29]Park, C., Review of Chemical-Kinetic Problems of Future NASA Mission, I: Earth Entries, J. Thermophys. Heat Transfer, Vol. 7(1993), pp. 385398.
[30] Argonne National Laboratory: PETSc. Portable, Extensible Toolkit for Scientific Computation,, 2004.
[31]Prabhu, R. K., An implementation of a Chemical and Thermal Nonequilibrium Flow Solver on Unstructured Meshes and Application to Blunt Bodies, NASA Contractor Report 194967, Lockheed Engineering and Sciences Co., Hampton, VA, August 1994.
[32]Ricchiuto, M., Construction and Analysis of Compact Resdidual Discretizations for Conservation Laws on Unstructured Meshes, Ph.D. thesis, Université Libre de Bruxelles, 2005.
[33]Ricchiuto, M., Villedieu, N., Abgrall, R., and Deconinck, H., On uniformly high order accurate residual distribution schemes for advection-diffusion, J. Comput. Applied Math., Vol. 215(2007), pp. 547556.
[34]Sarma, G. S. R., Physico-chemical modeling in hypersonic flow simulation, Prog. Aerospace Sci., pp. 281349, 1958.
[35]Sutton, K. and Gnoffo, P. A., Multi-component diffusion with application to computational aerothermodynamics, Technical Paper 98-2575, AIAA, Albuquerque, New Mexico, June 1998.
[36]Van der Weide, E., Deconinck, H., Issmann, E., Degrez, G., A parallel implicit multidimensional upwind residual distribution method forthe Navier-Stokes equations on unstructured grids, J. Comp. Mech., Vol. 23(1999), No. 2, pp. 199208.
[37]Van der Weide, E., Compressible Flow Simulation on Unstructured Grids using Multidimensional Upwind Schemes, Ph.D. thesis, Delft University of Technology, Netherlands, 1998.
[38]Yos, J. M., Approximate equations for the viscosity and translational thermal conductivity of gas mixtures, Contract Report AVSSD-0112-67-RM, AVCO Corp., Wilmington, MA, 1967.


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Conservative Residual Distribution Method for Viscous Double Cone Flows in Thermochemical Nonequilibrium

  • Andrea Lani (a1), Marco Panesi (a2) and Herman Deconinck (a1)


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