Skip to main content Accessibility help
×
Home
  • Print publication year: 2016
  • Online publication date: June 2016

4 - Numerical Methods

Related content

Powered by UNSILO
ABGRALL, R. 1994. On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. Journal of Computational Physics, 114(1), 45–58.
ACHARYA, S. & JANG, D. 1988. Source term decomposition to improve convergence of swirling flow calculations. AIAA Journal, 26(3), 372–374.
AGARWAL, A. & MORRIS, P. J. 2000. Direct simulation of acoustic scattering by a rotorcraft fuselage. In Proceedings of Sixth AIAA/CEAS Aeroacoustics Conference, Lahaina, Hawaii, 12–14 June, AIAA Paper No. AIAA-2000-2030.
ANG, W.-T. 2007. A beginner's course in boundary element methods, Universal-Publishers.
ARAKAWA, A. 1966. Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow, Part I. Journal of Computational Physics, 1(1), 119–143.
ARMSTRONG, D. B., NAJAFI-YAZDI, A., MONGEAU, L. & RAYMOND, V. 2013. Numerical simulations of flow over a landing gear with noise reduction devices using the lattice-boltzmann method. AIAA Paper No. AIAA-2013-2114.
ASCHER, U. M. & PETZOLD, L. R. 1998. Computer methods for ordinary differential equations and differential-algebraic equations, Vol. 61, Society of Industrial and Applied Mathematics (SIAM).
ASHCROFT, G. Z. 2001. A computational investigation of the noise radiated by flow induced cavity oscillations. AIAA 39th Aerospace Sciences Meeting, January 9–11, AIAA Paper No. AIAA- 2001-0512.
ASHCROFT, G. & ZHANG, X. 2001. A computational investigation of the noise radiated by flow-induced cavity oscillations. Proccedings 39th Aerospace Sciences Meeting and Exhibit, January, AIAA Paper 2001-0512.
ATKINS, H. L. & LOCKARD, D. P. 1999. A high-order method using unstructured grids for the aeroacoustic analysis of realistic aircraft configurations. In 5th AIAA/CEAS Aeroacoustics Conference and Exhibit, May, AIAA Paper No. AIAA-1999–1945.
BARTH, T. J. & JESPERSEN, D. 1989. The design and application of upwind schemes on unstructured meshes, 27th Aerospace Sciences Meeting, Reno, Nevada, January 9-12, AIAA Paper No. AIAA-1989-0366.
BARTON, I. 1998a. Comparison of SIMPLE‐ and PISO‐type algorithms for transient flows. International Journal for Numerical Methods in Fluids, 26, 459–483.
BARTON, I. 1998b. Improved laminar predictions using a stabilised time‐dependent simple scheme. International Journal for Numerical Methods in Fluids, 28, 841–857.
BEAM, R. M. & WARMING, R. F. 1976. An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. Journal of Computational Physics, 22(1), 87–110.
BEAM, R. M. & WARMING, R. F. 1982. Implicit numerical methods for the compressible Navier-Stokes and Euler equations. In Von Karman Inst. for Fluid Dyn. Computational Fluid Dyn., 99 (SEE N83-19024 09-34), 1.
BELL, B. C. & SURANA, K. S. 1994. A space-time coupled p-version least-squares finite element formulation for unsteady fluid dynamics problems. International Journal for Numerical Methods in Engineering, 37(20), 3545–3569.
BHATNAGAR, P. L., GROSS, E. P. & KROOK, M. 1954. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical Review, 94(3), 511.
BIRKEFELD, A. & MUNZ, C. 2012. Simulations of airfoil noise with the discontinuous Galerkin solver NoisSol. ERCOFTAC Bull, 90, 28–33.
BLAISDELL, G., SPYROPOULOS, E. & QIN, J. 1996. The effect of the formulation of nonlinear terms on aliasing errors in spectral methods. Applied Numerical Mathematics, 21(3), 207–219.
BLAZEK, J., KROLL, N., RADESPIEL, R. AND ROSSOW, C. C. 1991. Upwind implicit residual smoothing method for multistage schemes, AIAA Tenth Computational Fluid Dynamics Conference, AIAA Paper No. AIAA-91-1533.
BLAZEK, J. 2005. Computational Fluid Dynamics: Principles and Applications, Elsevier.
BOGEY, C. & BAILLY, C. 2004. A family of low dispersive and low dissipative explicit schemes for flow and noise computations. Journal of Computational Physics, 194(1), 194–214.
BOOK, D. L., BORIS, J. P. & HAIN, K. 1975. Flux-corrected transport II: Generalizations of the method. Journal of Computational Physics, 18(3), 248–283.
BORIS, J. P. & BOOK, D. L. 1973. Flux-corrected transport I: SHASTA, A fluid transport algorithm that works. Journal of Computational Physics, 11(1), 38–69.
BRANDT, A. 1977. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation, 31, 333–390.
BRANDT, A. 1980. Multilevel adaptive computations in fluid dynamics. AIAA Journal, 18(10), 1165–1172.
BRES, G. A., PÉROT, F. & FREED, D. 2009. Properties of the lattice-Boltzmann method for acoustics. Proc. AIAA Aeroacoustics Conference, Miami, Florida, AIAA Paper No. AIAA-2009-3395.
BRILEY, W. & MCDONALD, H. 1975. Solution of the three-dimensional compressible Navier-Stokes equations by an implicit technique. Proceedings of the Fourth International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, Springer-Verlag, Berlin, 35, 105–110.
BROECKHOVEN, J. R. & LACOR, C. 2007. Large-eddy simulation for acoustics. In WAGNER, C. A., HUTTL, T. & SAGAUT, P. (eds.), Cambridge University Press.
CAMACHO, R. & BARBOSA, J. 2005. The boundary element method applied to incompressible viscous fluid flow. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 27, 456–462.
CAMPOBASSO, M. S. & GILES, M. B. 2003. Effects of flow instabilities on the linear analysis of turbomachinery aeroelasticity. Journal of Propulsion and Power, 19(2), 250–259.
CAMPOBASSO, M. S. & GILES, M. B. 2004. Stabilization of a linear flow solver for turbomachinery aeroelasticity using recursive projection method. AIAA Journal, 42(9), 1765–1774.
CARTON, D. W., HILLEWAERT, K. & GEUZAINE, P. 2012. DNS of a low pressure turbine blade computed with the discontinuous Galerkin method. ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, ASME Paper No. 2101-2111.
CHAPMAN, M. 1981. FRAM – Nonlinear damping algorithms for the continuity equation. Journal of Computational Physics, 44(1), 84–103.
CHEN, C.-J., NASERI-NESHAT, H. & HO, K.-S. 1981. Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow. Numerical Heat Transfer, 4, 179–197.
CHESSHIRE, G. & HENSHAW, W. D. 1990. Composite overlapping meshes for the solution of partial differential equations. Journal of Computational Physics, 90(1), 1–64.
CHOI, H. & MOIN, P. 1994. Effects of the computational time step on numerical solutions of turbulent flow. Journal of Computational Physics, 113, 1–4.
CHOI, S. K. 1999. Note on the use of momentum interpolation method for unsteady flows. Numerical Heat Transfer, Part A: Applications, 36, 545–550.
CHOI, Y. & MERKLE, C. L. 1991. Time-derivative preconditioning for viscous flows. AIAA 22nd Fluid Dynamics Conference, Paper No. AIAA-91-1652.
CHORIN, A. J. 1967. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics, 2(1), 12–26.
CHOW, F. K. & MOIN, P. 2003. A further study of numerical errors in large-eddy simulations. Journal of Computational Physics, 184(2), 366–380.
CHUNG, Y. M. & TUCKER, P. G. 2003. Accuracy of higher-order finite difference schemes on nonuniform grids. AIAA Journal, 41(8), 1609–1611.
CIARDI, M., SAGAUT, P., KLEIN, M. & DAWES, W. 2005. A dynamic finite volume scheme for large-eddy simulation on unstructured grids. Journal of Computational Physics, 210(2), 632–655.
COLONIUS, T. & LELE, S. K. 2004. Computational aeroacoustics: progress on nonlinear problems of sound generation. Progress in Aerospace Sciences, 40(6), 345–416.
COUGHLIN, G. 2010. On hexahedral meshing for complex geometry. MPhil Thesis, University of Cambridge.
CROWLEY, W. 1967. Second-order numerical advection. Journal of Computational Physics, 1(4), 471–484.
DAUDE, F., BERLAND, J., EMMERT, T., LAFON, P., CROUZET, F. & BAILLY, C. 2012. A high-order finite-difference algorithm for direct computation of aerodynamic sound. Computers & Fluids, 61, 46–63.
DAVIES, C. & CARPENTER, P. W. 2001. A novel velocity-vorticity formulation of the Navier-Stokes equations with applications to boundary layer disturbance evolution. Journal of Computational Physics, 172(1), 119–165.
DAVIS, R. & MOORE, E. 1982. A numerical study of vortex shedding from rectangles. Journal of Fluid Mechanics, 116(3), 475–506.
DEARDORFF, J. W. 1970. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. Journal of Fluid Mechanics, 41(2), 453–480.
DELANAYE, M. & ESSERS, J. 1997. Finite volume scheme with quadratic reconstruction on unstructured adaptive meshes applied to turbomachinery flows. Journal of Turbomachinery, 119(2), 263–269.
DEMIRDŽIĆ, I., LILEK, Ž. & PERIĆ, M. 1993. A collocated finite volume method for predicting flows at all speeds. International Journal for Numerical Methods in Fluids, 16, 1029–1050.
DEMIRDZIC, I. & PERIC, M. 1988. Space conservation law in finite volume calculations of fluid flow. International Journal for Numerical Methods in Fluids, 8(9), 1037–1050.
DENTON, J. D. 1992. The calculation of three-dimensional viscous flow through multistage turbomachines. Journal of Turbomachinery, 114(1), 18–26.
DOUGLAS, J. & GUNN, J. E. 1964. A general formulation of alternating direction methods. Numerische Mathematik, 6, 428–453.
DUCROS, F., FERRAND, V., NICOUD, F., WEBER, C., DARRACQ, D., GACHERIEU, C. & POINSOT, T. 1999. Large-eddy simulation of the shock/turbulence interaction. Journal of Computational Physics, 152(2), 517–549.
DUCROS, F., LAPORTE, F., SOULERES, T., GUINOT, V., MOINAT, P. & 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.
DUKOWICZ, J. & RAMSHAW, J. 1979. Tensor viscosity method for convection in numerical fluid dynamics. Journal of Computational Physics, 32(1), 71–79.
ENGELMAN, M. & SANI, R. 1986. Finite element simulation of incompressible fluid flows with a free/moving surface. Recent Advances in Numerical Methods in Fluids, 5, 47–74.
FARES, E. & NOLTING, S. 2011. Unsteady flow simulation of a high-lift configuration using a lattice Boltzmann approach. Proceedings of the forty ninth AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA Paper No. AIAA-2011-869.
FERZIGER, J. H. & PERIC, M. 2002. Computational methods for fluid dynamics, Vol. 3, Springer.
FLETCHER, C. A. 1988. Computational techniques for fluid dynamics. Vol. 1: Fundamental and general techniques, Springer.
FLETCHER, C. A. 1998. Computational Techniques for Fluid Dynamics, Vol. 1, Springer-Verlag.
FRINK, N. T. 1994. Recent progress toward a three-dimensional unstructured Navier-Stokes flow solver. Proceedings AIAA, 32nd Aerospace Sciences Meeting & Exhibit, Reno, Nevada. AIAA Paper No. AIAA-1994-0061
FRINK, N. T., PARIKH, P. & PIRZADEH, S. 1991. A fast upwind solver for the Euler equations on three-dimensional unstructured meshes. Proceedings 29th Aerospace Sciences Meeting. January AIAA paper No. 1991-0102.
FRITSCH, G. & GILES, M. 1992. Second-order effects of unsteadiness on the performance of turbomachines. 37th International Gas Turbine and Aeroengine Congress and Exposition, ASME Paper No. GT-32-389.
GAMET, L., DUCROS, F., NICOUD, F., POINSOT, T., et al. 1999. Compact finite difference schemes on non-uniform meshes: Application to direct numerical simulations of compressible flows. International Journal for Numerical Methods in Fluids, 29(2), 159–191.
GHOSAL, S. 1996. An analysis of numerical errors in large-eddy simulations of turbulence. Journal of Computational Physics, 125(1), 187–206.
GILES, M. 2004. The Hydra user's guide. Version 6, Rolls-Royce Plc.
GILES, M. B. 1990. Nonreflecting boundary conditions for Euler equation calculations. AIAA Journal, 28(12), 2050–2058.
GILES, M. B. 1988. Calculation of unsteady wake/rotor interaction, Journal of Propulsion and Power, 4(4), 356–362.
GILES, M. B. 1991. UNSFLO: A numerical method for the calculation of unsteady flow in turbomachinery, Gas Turbine Laboratory Report, Massachusetts Institute of Technology, Report No. 205.
GINGOLD, R. A. & MONAGHAN, J. J. 1977. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181, 375–389.
GLASS, J. & RODI, W. 1982. A higher order numerical scheme for scalar transport. Computer Methods in Applied Mechanics and Engineering, 31(3), 337–358.
GODUNOV, S. K. 1959. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Matematicheskii Sbornik, 89(3), 271–306.
GOSMAN, A., KOOSINLIN, M., LOCKWOOD, F. & SPALDING, D. 1976. Transfer of heat in rotating systems. Gas Turbine Conference and Products Show, ASME Paper No. 76-GT-25.
GRESHO, P., LEE, R. & SANI, R. 1980. On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions. In TAYLOR, C. & MORGAN, K. (eds.), Recent Advances in Numerical Methods in Fluids, 27–79, Pineridge Press, Ltd.
GRESHO, P. M., CHAN, S. T., LEE, R. L. & UPSON, C. D. 1984. A modified finite element method for solving the time-dependent, incompressible Navier-Stokes equations, Part 1: Theory. International Journal for Numerical Methods in Fluids, 4(6), 557–598.
GRINSTEIN, F. F., MARGOLIN, L. G. & RIDER, W. J. 2011. Implicit Large Eddy Simulation – Computing Turbulent Fluid Dynamics, Cambridge University Press.
HARLOW, F. H. & AMSDEN, A. A. 1971. A numerical fluid dynamics calculation method for all flow speeds. Journal of Computational Physics, 8, 197–213.
HARLOW, F. H. & WELCH, J. E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 8(12), 2182.
HARTEN, A. 1983. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49(3), 357–393.
HARTEN, A., ENGQUIST, B., OSHER, S. & CHAKRAVARTHY, S. R. 1987. Uniformly high order accurate essentially non-oscillatory schemes, III. Journal of Computational Physics, 71(2), 231–303.
HASSAN, Y. A., RICE, J. G. & KIM, J. 1983. A stable mass-flow-weighted two-dimensional skew upwind scheme. Numerical Heat Transfer, 6, 395–408.
HE, L. & WANG, D. 2011. Concurrent blade aerodynamic-aero-elastic design optimization using adjoint method. Journal of Turbomachinery, 133(1), 011021.
HEDGES, L., TRAVIN, A. & SPALART, P. 2002. Detached-eddy simulations over a simplified landing gear. Journal of Fluids Engineering, 124(2), 413–423.
HENKES, R. A. 1990. Natural-convection boundary layers. Ph.D. dissertation, Technische University Delft.
HICKEN, J. E. & ZINGG, D. W. 2008. Parallel newton-krylov solver for the euler equations discretized using simultaneous approximation terms. AIAA Journal, 46(11), 2773–2786.
HIGNETT, B. P., WHITE, A., CARTER, R., JACKSON, W. & SMALL, R. 1985. A comparison of laboratory measurements and numerical simulations of baroclinic wave flows in a rotating cylindrical annulus. Quarterly Journal of the Royal Meteorological Society, 111(467), 131–154.
HIRSCH, C. 2007. Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics: The Fundamentals of Computational Fluid Dynamics, Vol. 1 and 2, Butterworth-Heinemann.
HIRT, C. 1968. Heuristic stability theory for finite-difference equations. Journal of Computational Physics, 2(4), 339–355.
HIRT, C., AMSDEN, A. A. & COOK, J. 1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics, 14(3), 227–253.
HIXON, R. 2000. Prefactored small-stencil compact schemes. Journal of Computational Physics, 165(2), 522–541.
HOLMES, D. & CONNELL, S. 1986. Solution of the 2D Navier-Stokes equations on unstructured adaptive grids. Ninth Computational Fluid Dynamics Conference, AIAA Paper No. 89–1932.
HOLMES, D., CONNELL, S. & ENGINES, G. A. 1989. Solution of the 2D Navier-Stokes equations on unstructured adaptive grids. Proceedings of the 9th Computational Fluid Dynamics Conference. AIAA Paper No. 89-1932-CP.
HORIUTI, K. & ITAMI, T. 1998. Truncation error analysis of the rotational form for the convective terms in the Navier–Stokes equation. Journal of Computational Physics, 145(2), 671–692.
HU, F., HUSSAINI, M. Y. & MANTHEY, J. 1996. Low-dissipation and low-dispersion Runge–Kutta schemes for computational acoustics. Journal of Computational Physics, 124(1), 177–191.
HU, X., & NICOLAIDES, R. 1992. Covolume techniques for anisotropic media. Numerische Mathematik, 61(1), 215–234.
HUJEIRAT, A. & RANNACHER, R. 1998. A method for computing compressible, highly stratified flows in astrophysics based on operator splitting. International Journal for Numerical Methods in Fluids, 28(1), 1–22.
HU, X. & NICOLAIDES, R. 1992. Covolume techniques for anisotropic media. Numerische Mathematik, 61, 215–234.
ISERLES, A. 1986. Generalized leapfrog methods. IMA Journal of Numerical Analysis, 6(4), 381–392.
ISSA, R. I. 1986. Solution of the implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics, 62(1), 40–65.
ISSA, R. & OLIVEIRA, P. 1994. Numerical prediction of phase separation in two-phase flow through T-junctions. Computers & Fluids, 23, 347–372.
JAMES, I., JONAS, P. & FARNELL, L. 1981. A combined laboratory and numerical study of fully developed steady baroclinic waves in a cylindrical annulus. Quarterly Journal of the Royal Meteorological Society, 107(451), 51–78.
JAMESON, A. 1991. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. Proceedings of the tenth Computational Fluid Dynamics Conference, June, AIAA Paper No. AIAA-1991-1596.
JAMESON, A. 2008a. Formulation of kinetic energy preserving conservative schemes for gas dynamics and direct numerical simulation of one-dimensional viscous compressible flow in a shock tube using entropy and kinetic energy preserving schemes. Journal of Scientific Computing, 34(2), 188–208.
JAMESON, A. 2008b. The construction of discretely conservative finite volume schemes that also globally conserve energy or entropy. Journal of Scientific Computing, 34(2), 152–187.
JAMESON, A., SCHMIDT, W., TURKEL, E., et al. 1981. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. Proceedings 14th Fluid and Plasma Dynamics Conference, June AIAA Paper No. AIAA-1981-1259.
JEFFERSON-LOVEDAY, R. 2008. Numerical simulations of unsteady impinging jet flows. Ph.D. dissertation, Swansea University.
JONES, W. & MARQUIS, A. 1985. Calculation of axisymmetric recirculating flows with a second order turbulence model. Proceedings of the 5th Symposium on Turbulent Shear Flows, Cornell University, 20.1–20.11.
JOO, J. & DURBIN, P. 2009. Simulation of turbine blade trailing edge cooling. Journal of Fluids Engineering, 131(2), 021102.
NAKAHASHI, K., & TOGASHI, F. 2000. Unstructured overset grid method for flow simulation of complex multiple body problems. Proceedings of ICAS 2000 Congress, Paper No. ICAS0263.
KARABASOV, S. A. & GOLOVIZNIN, V. M. 2007. New efficient high-resolution method for nonlinear problems in aeroacoustics. AIAA Journal, 45(12), 2861–2871.
KARABASOV, S. & GOLOVIZNIN, V. 2009. Compact accurately boundary-adjusting high-resolution technique for fluid dynamics. Journal of Computational Physics, 228(19), 7426–7451.
KHATIR, Z. 2000. Discrete vortex modelling of near-wall flow structure in turbulent boundary layers. Ph.D. dissertation, The University of Warwick.
KIM, J. & MOIN, P. 1985. Application of a fractional-step method to incompressible Navier-Stokes equations. Journal of Computational Physics, 59(2), 308–323.
KIM, J. W. & LEE, D. J. 1996. Optimized compact finite difference schemes with maximum resolution. AIAA Journal, 34(5), 887–893.
KIRCHHART, M. 2013. Vortex methods. Handout for the CES-Seminar Talk.
KRAKOS, J. A. & DARMOFAL, D. L. 2010. Effect of small-scale output unsteadiness on adjoint-based sensitivity. AIAA Journal, 48(11), 2611–2623.
LACOR, C. 1999. Industrial computational fluid dynamics. von Karman Institute for Fluid Dynamics. May 31–June 4 (Eds. BUCHLIN, J.-M. & Ph. Planquart), VKI LS 1999-06.
LAIZET, S. & LAMBALLAIS, E. 2009. High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy. Journal of Computational Physics, 228(16), 5989–6015.
LEE, K. R., PARK, J. H. & KIM, K. H. 2011. High-order interpolation method for overset grid based on finite volume method. AIAA Journal, 49(7), 1387–1398.
LEITH, C. E. 1965. Numerical simulation of the earth's atmosphere. Meth. Comp. Phys, 4, 1–28.
LELE, S. K. 1992. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103(1), 16–42.
LEONARD, B. P. 1979. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 19(1), 59–98.
LERAT, A. 1979. Une classe de schémas aux différences implicites pour les systèmes hyperboliques de lois de conservation. Comptes Rendus Acad. Sciences Paris, 288, 1033–1036.
LIEN, F.-S. & LESCHZINER, M. 1994. Upstream monotonic interpolation for scalar transport with application to complex turbulent flows. International Journal for Numerical Methods in Fluids, 19(6), 527–548.
LIOU, M.-S. & STEFFEN JR, C. J. 1993. A new flux splitting scheme. Journal of Computational Physics, 107(1), 23–39.
LIU, X.-D., OSHER, S. & CHAN, T. 1994. Weighted essentially non-oscillatory schemes. Journal of Computational Physics, 115, 200–212.
LIU, Y. & NISHIMURA, N. 2006. The fast multipole boundary element method for potential problems: a tutorial. Engineering Analysis with Boundary Elements, 30, 371–381.
LOCKARD, D. P., BRENTNER, K. S. & ATKINS, H. 1995. High-accuracy algorithms for computational aeroacoustics. AIAA Journal, 33(2), 246–251.
LU, Y., YUAN, X. & DAWES, W. 2012. Investigation of 3D internal flow using new flux-reconstruction high order method. ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, 2195–2216.
MAJUMDAR, S. 1988. Role of underrelaxation in momentum interpolation for calculation of flow with nonstaggered grids. Numerical Heat Transfer, 13, 125–132.
MANGANI, L., DARWISH, M. & MOUKALLED, F. 2013. Development of a Novel Pressure-Based Coupled CFD Solver for Turbulent Compressible Flows in Turbomachinery Applications. American Society of Mechanical Engineers 2013 Fluids Engineering Division Summer Meeting, Paper No. FEDSM2013-16082.
MANI, K. & MAVRIPLIS, D. J. 2010. Spatially non-uniform time-step adaptation for functional outputs in unsteady flow problems. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper No. AIAA-2010-121.
MANOHA, E., TROFF, B. & SAGAUT, P. 2000. Trailing-edge noise prediction using large-eddy simulation and acoustic analogy. AIAA Journal, 38(4), 575–583.
MARIÉ, S., RICOT, D. & SAGAUT, P. 2009. Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics. Journal of Computational Physics, 228, 1056–1070.
MARONGIU, J., LEBOEUF, F. & PARKINSON, E. 2007. Numerical simulation of the flow in a Pelton turbine using the meshless method smoothed particle hydrodynamics: A new simple solid boundary treatment. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 221(6), 849–856.
MARONGIU, J.-C., LEBOEUF, F., CARO, J. & PARKINSON, E. 2010. Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method. Journal of Hydraulic Research, 48(S1), 40–49.
MARY, I. & SAGAUT, P. 2002. Large eddy simulation of flow around an airfoil near stall. AIAA Journal, 40(6), 1139–1145.
MASON, P. J. & CALLEN, N. S. 1986. On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow. Journal of Fluid Mechanics, 162, 439–462.
MOINIER, P. 1999. Algorithm developments for an unstructured viscous flow solver. Ph.D. dissertation, Oxford University.
MOSAHEBI, A. & NADARAJAH, S. K. 2011. An implicit adaptive non-linear frequency domain method (pNLFD) for viscous periodic steady state flows on deformable grids. Proceedings of the 49th Aerospace Sciences Meeting, January, Orlando, Florida, Paper No. AIAA-2011-775.
MOULINEC, C., BENHAMADOUCHE, S., LAURENCE, D. & PERIC, M. 2005. LES in a U-bend pipe meshed by polyhedral cells. Engineering Turbulence Modelling and Experiments, 6, 237–246.
MURAMATSU, T., & NINOKATA, H., 1992. Thermal striping temperature fluctuation analysis using the algebraic stress turbulence model in water and sodium, Japan Society of Mechanical Engineers International Journal, Series 2, 35(4), 486–496.
NASSER, A. & LESCHZINER, M. 1985. Computation of transient recirculating flow using spline approximations and time-space characteristics. Proceedings of the 4th International Conference on Numerical Methods in Laminar and Turbulent Flow, Swansea, 480–491.
NOWAK, A. & BREBBIA, C. 1989. The multiple-reciprocity method: A new approach for transforming BEM domain integrals to the boundary. Engineering Analysis with Boundary Elements, 6, 164–167.
ORKWIS, P. D., TURNER, M. G. & BARTER, J. W. 2002. Linear deterministic source terms for hot streak simulations. Journal of Propulsion and Power, 18(2), 383–389.
ORKWIS, P. D. & VANDEN, K. J.. On the accuracy of numerical versus analytical Jacobians. Proceedings 32nd AIAA, Aerospace Sciences Meeting & Exhibit, Reno, Nevada, AIAA Paper 94-0176.
ORSZAG, S. A. 1971. Accurate solution of the Orr–Sommerfeld stability equation. Journal of Fluid Mechanics, 50(04), 689–703.
OZYORUK, Y. & LONG, L. N. 1997. Multigrid acceleration of a high-resolution. AIAA Journal, 35(3), 428–433.
PARTRIDGE, P. W., BREBBIA, C. A. & WROBEL, L. C. 1992. The dual reciprocity boundary element method, Computational Mechanics Publications.
PATANKAR, S. 1980. Numerical heat transfer and fluid flow, CRC Press.
PATANKAR, S. & BALIGA, B. 1978. A new finite-difference scheme for parabolic differential equations. Numerical Heat Transfer, 1(1), 27–37.
PATANKAR, S. V. & SPALDING, D. B. 1972. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15(10), 1787–1806.
PATERA, A. T. 1984. A spectral element method for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics, 54(3), 468–488.
PAULEY, L. L., MOIN, P. & REYNOLDS, W. C. 1990. The structure of two-dimensional separation. Journal of Fluid Mechanics, 220, 397–411.
PEACEMAN, D. W. & RACHFORD, J. 1955. The numerical solution of parabolic and elliptic differential equations. Journal of the Society for Industrial & Applied Mathematics, 3, 28–41.
PINELLI, A., NAQAVI, I., PIOMELLI, U. & FAVIER, J. 2010. Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers. Journal of Computational Physics, 229(24), 9073–9091.
PITSCH, H. 2006. Large-eddy simulation of turbulent combustion. Annual Review of Fluid Mechanics, 38, 453–482.
PREECE, A. 2008. An Investigation into Methods to aid the Simulation of Turbulent Separation Control. Ph.D. dissertation, The University of Warwick.
RAITHBY, G. & SCHNEIDER, G. 1979. Numerical solution of problems in incompressible fluid flow: treatment of the velocity-pressure coupling. Numerical Heat Transfer, Part A: Applications, 2, 417–440.
RAITHBY, G. & SCHNEIDER, G. 1980. Erratum. Numerical Heat Transfer, 3, 513.
RAW, M. 1996. Robustness of coupled algebraic multigrid for the Navier-Stokes equations. Proceedings 34th Aerospace Sciences Meeting and Exhibit, January, AIAA Paper No., AIAA-96-0297.
RAYNER, D. 1993. A Numerical Study into the Heat Transfer beneath the Stator Blade of an Axial Compressor. Ph.D. dissertation, University of Sussex.
REINDL, D. T., BECKHAM, W. A., MITCHELL, J. W. & RUTLAND, C. 1991. Benchmarking transient natural convection in an enclosure, ASME Paper No. 91-HT-8, pp. 1–7.
RHIE, C. & CHOW, W. 1983. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 21, 1525–1532.
RIDER, W. & DRIKAKIS, D. 2005. High-resolution methods for incompressible and low-speed flows, Springer.
RIZZETTA, D. P., VISBAL, M. R. & MORGAN, P. E. 2008. A high-order compact finite-difference scheme for large-eddy simulation of active flow control. Progress in Aerospace Sciences, 44(6), 397–426.
ROACHE, P. J. 1992. A flux-based modified method of characteristics. International Journal for Numerical Methods in Fluids, 15(11), 1259–1275.
ROE, P. 1986. Characteristic-based schemes for the Euler equations. Annual Review of Fluid Mechanics, 18(1), 337–365.
ROE, P. L. 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43(2), 357–372.
ROGERS, S. E. & KWAK, D. 1990. Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations. AIAA Journal, 28(2), 253–262.
ROGERS, S. E., KWAK, D. & CHANG, J. L. 1986. Numerical solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. NASA STI/Recon Technical Report N, 87, 11964.
RUGE, J. & STUEBEN, K. 1986. Algebraic multigrid. Arbeitspapiere der GMD, 210.
RUMPFKEIL, M. P., ZINGG, D. W. 2007. A general framework for the optimal control of unsteady flows with applications. Proceedings of the 45th AIAA Aerospace Meeting and Exhibit, 8–11 January, Reno, Nevada, Paper No. AIAA 2007–1128.
SANDHAM, N. & YEE, H. 2001. Entropy splitting for high order numerical simulation of compressible turbulence. In Computational Fluid Dynamics, 361–366, Springer.
SEGERLIND, L. 1984. Applied Finite Element Analysis, John Wiley and Sons.
SEIDL, V., PERIC, M. & SCHMIDT, M. 1995. Space- and time-parallel Navier-Stokes solver for 3d block-adaptive Cartesian grids. Parallel Computational Fluid Dynamics: Proceedings, 95, 557–584.
SHUR, M., SPALART, P., STRELETS, M. K. & TRAVIN, A. 2003. Towards the prediction of noise from jet engines. International Journal of Heat and Fluid Flow, 24(4), 551–561.
SKELBOE, S. 1977. The control of order and steplength for backward differentiation methods. BIT Numerical Mathematics, 17(1), 91–107.
SPALART, P., HEDGES, L., SHUR, M. & TRAVIN, A. 2003. Simulation of active flow control on a stalled airfoil. Flow, Turbulence and Combustion, 71(1–4), 361–373.
SPALDING, D. 1972. A novel finite difference formulation for differential expressions involving both first and second derivatives. International Journal for Numerical Methods in Engineering, 4, 551–561.
SPEZIALE, C. G. 1987. On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics. Journal of Computational Physics, 73(2), 476–480.
SPYROPOULOS, E. T. & BLAISDELL, G. A. 1998. Large-eddy simulation of a spatially evolving supersonic turbulent boundary-layer flow. AIAA Journal, 36(11), 1983–1990.
STANIFORTH, A. & COTE, J. 1991. Semi-Lagrangian integration schemes for atmospheric models – a review. Monthly Weather Review, 119(9), 2206–2223.
STONE, H. L. 1968. Iterative solution of implicit approximations of multidimensional partial differential equations. Society for Industrial and Applied Mathematics Journal on Numerical Analysis, 5, 530–558.
SUCCI, S. 2001. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press.
SWANSON, R. C. & TURKEL, E. 1992. On central-difference and upwind schemes. Journal of Computational Physics, 101(2), 292–306.
TAJALLIPOUR, N., BABAEE OWLAM, B. & PARASCHIVOIU, M. 2009. Self-adaptive upwinding for large eddy simulation of turbulent flows on unstructured elements. Journal of Aircraft, 46(3), 915–926.
TALHA, T. 2012. A numerical investigation of three-dimensional unsteady turbulent channel flow subjected to temporal acceleration. Ph.D. dissertation, University of Warwick.
TAM, C. K. & SHEN, H. 1993. Direct computation of nonlinear acoustic pulses using high order finite difference schemes. Proceedings 15th Aeroacoustics Conference. October AIAA Paper No., AIAA-93-4325.
TAM, C. K. & WEBB, J. C. 1993. Dispersion-relation-preserving finite difference schemes for computational acoustics. Journal of Computational Physics, 107(2), 262–281.
TAM, C. K., WEBB, J. C. & DONG, Z. 1993. A study of the short wave components in computational acoustics. Journal of Computational Acoustics, 1(1), 1–30.
TANG, L. & BAEDER, J. D. 1998. Uniformly accurate finite difference schemes for p-refinement. SIAM Journal on Scientific Computing, 20(3), 1115–1131.
THOMAS, P. & LOMBARD, C. 1979. Geometric conservation law and its application to flow computations on moving grids. AIAA Journal, 17(10), 1030–1037.
TU, C., DEVILLE, M., DHEUR, L. & VANDERSCHUREN, L. 1992. Finite element simulation of pulsatile flow through arterial stenosis. Journal of Biomechanics, 25(10), 1141–1152.
TUCKER, P. 1997. Numerical precision and dissipation errors in rotating flows. International Journal of Numerical Methods for Heat & Fluid Flow, 7(7), 647–658.
TUCKER, P. G. 2001. Computation of unsteady internal flows, Springer.
TUCKER, P. 2002a. Novel multigrid orientated solution adaptive time-step approaches. International Journal for Numerical Methods in Fluids, 40(3–4), 507–519.
TUCKER, P. G. 2002b. Temporal behavior of flow in rotating cavities. Numerical Heat Transfer: Part A: Applications, 41(6–7), 611–627.
TUCKER, P. G. 2004. Novel MILES computations for jet flows and noise. International Journal of Heat and Fluid Flow, 25(4), 625–635.
TUCKER, P. G. 2013. Unsteady computational fluid dynamics in aeronautics, Springer.
UZUN, A. & HUSSAINI, M. Y. 2009. Simulation of noise generation in the near-nozzle region of a chevron nozzle jet. AIAA Journal, 47(8), 1793–1810.
VAN ALBADA, G., VAN LEER, B. & ROBERTS JR, W. 1982. A comparative study of computational methods in cosmic gas dynamics. Astronomy and Astrophysics, 108, 76–84.
VAN DOORMAAL, J. & RAITHBY, G. 1984. Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numerical Heat Transfer, 7, 147–157.
VAN LEER, B. 1974. Towards the ultimate conservative difference scheme, II: Monotonicity and conservation combined in a second-order scheme. Journal of Computational Physics, 14(4), 361–370.
VAN LEER, B. 1977. Towards the ultimate conservative difference scheme, III: Upstream-centered finite-difference schemes for ideal compressible flow. Journal of Computational Physics, 23(3), 263–275.
VAN LEER, B. 1979. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. Journal of Computational Physics, 32(1), 101–136.
VAUGHAN, C., GILHAM, S. & CHEW, J. 1989. Numerical solutions of rotating disc flows using a non-linear multigrid algorithm. Proceedings of the 6th International Conference on Numerical Methods in Laminar and Turbulent Flow, 63–67.
VERMEIRE, B. C., NADARAJAH, S. & TUCKER, P. G. 2014. Canonical test cases for high-order unstructured implicit large eddy simulation. Proceedings 52nd AIAA Aerospace Sciences Meeting, AIAA Paper No. AIAA-2014-0935.
VISBAL, M. R. & GAITONDE, D. V. 2002. On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. Journal of Computational Physics, 181(1), 155–185.
WALLIS, S. G. & MANSON, J. R. 1997. Accurate numerical simulation of advection using large time steps. International Journal for Numerical Methods in Fluids, 24(2), 127–139.
WANG, Z. J., LIU, Y., MAY, G., & JAMESON, A., 2007. Spectral difference method for unstructured grids II: extension to the Euler equations. Journal of Scientific Computing, 32(1), 45–71.
WATERSON, N. P. & DECONINCK, H. 1995. A unified approach to the design and application of bounded higher-order convection schemes. Numerical Methods in Laminar and Turbulent Flow, 9, 203–214.
WATSON, R. 2014. Large eddy simulation of cutback trailing edges for film cooling turbine blades. Ph.D. dissertation, University of Cambridge.
WEISS, J. M. & SMITH, W. A. 1995. Preconditioning applied to variable and constant density flows. AIAA Journal, 33(11), 2050–2057.
WIETH, L., LIEBER, C., KURZ, W., BRAUN, S., KOCH, R., & BAUER, H. J. 2015. Numerical modeling of an aero-engine bearing chamber using the meshless smoothed particle hydrodynamics method. ASME Turbo Expo 2015, Turbine Technical Conference and Exposition, Montreal, Canada, ASME Paper No. Paper No. GT2015-42316.
WILLCOX, D. 1998. Turbulence modelling for CFD, DCW Industries Inc.
WOLF, W. & AZEVEDO, J. 2007. High-order ENO and WENO schemes for unstructured grids. International Journal for Numerical Methods in Fluids, 55(10), 917–943.
XIA, H. 2005. Dynamic Grid Detached-Eddy Simulation for Synthetic Jet Flows. Ph.D. dissertation, The University of Sheffield.
YANG, G., CAUSON, D., INGRAM, D., SAUNDERS, R. & BATTEN, P. 1997. A Cartesian cut cell method for compressible flows, Part B: moving body problems. Aeronautical Journal, 101(1002), 57–65.
YAO, Y., SAVILL, A., SANDHAM, N. & DAWES, W. 2000. Simulation of a turbulent trailing-edge flow using unsteady RANS and DNS. In NAGANO, Y., HANJALIC, K. & TSUJI, T. (eds.), Turbulence, Heat and Mass Transfer, 463–470, Aichi Shuppan.
YU, B., TAO, W.-Q., WEI, J.-J., KAWAGUCHI, Y., TAGAWA, T. & OZOE, H. 2002. Discussion on momentum interpolation method for collocated grids of incompressible flow. Numerical Heat Transfer, Part B: Fundamentals, 42, 141–166.
ZHU, Z. W., LACOR, C. & HIRSCH, C.. A new residual smoothing method for multigrid multi-stage schemes. Proceedings of the 11th AIAA CFD Conference, Paper No. AIAA-93-3356.
ZIENKIEWICZ, O. C. & TAYLOR, R. L. 2005. The finite element method for solid and structural mechanics, Butterworth-Heinemann.
ZIENKIEWICZ, O., TAYLOR, R. & NITHIARASU, P. 2005. The Finite Element Method for Fluid Dynamics, Sixth Edition, Elsevier.
ZOLTAK, J. & DRIKAKIS, D. 1998. Hybrid upwind methods for the simulation of unsteady shock-wave diffraction over a cylinder. Computer Methods in Applied Mechanics and Engineering, 162(1), 165–185.