Skip to main content Accessibility help
  • Print publication year: 2017
  • Online publication date: October 2017


Abramowitz, M. and Stegun, I. (eds.)(1965). Handbook of Mathematical Functions. Dover Publications.
Akiki, G. and Balachandar, S.(2016). Immersed boundary method with non- uniform distribution of Lagrangian markers for a non-uniform Eulerian mesh. J. Comp. Phys. 307, 34–59
Almgren, A.S., Bell, J.B., Colella, P. and Marthaler, T. (1997). A Cartesian grid projection method for the incompressible Euler equations in complex geome- tries. SIAM J. Sci. Comput. 18, 1289.
Anderson, S.L. (1990). Random number generation on vector supercomputers and other advanced architectures. SIAM Rev. 32, 221–51
Aref, H. (1979). Motion of three vortices. Phys. Fluids 22, 393–400
Aref, H. (1982). Point vortex motions with a center of symmetry. Phys. Fluids 25, 2183–7
Aref, H. (1983). Integrable, chaotic and turbulent vortex motion in two- dimensional flows. Ann. Rev. Fluid Mech. 15, 345–89
Aref, H. (1984). Stirring by chaotic advection. J. Fluid Mech. 143, 1–21
Aref, H. (2002). The development of chaotic advection. Phys. Fluids 14, 1315–25
Aref, H. and Balachandar, S. (1986). Chaotic advection in a Stokes flow. Phys. Fluids 29, 3515–21
Aref, H. and Jones, S.W. (1993). Chaotic motion of a solid through ideal fluid. Phys. Fluids 5, 3026–8
Aref, H., Jones, S.W., Mofina, S. and Zawadzki, I. (1989). Vortices, kinematics and chaos. Physica D 37, 423–40
Aref, H., Rott, N. and Thomann, H. (1992). Grobli's solution of the three-vortex problem. Ann. Rev. Fluid Mech. 24, 1–20
Arnold, V.I. (1978). Mathematical Methods of Classical Mechanics. Springer.
Arnold, V.I. and Avez, A. (1968). Ergodic Problems of Classical Mechanics. W.A. Benjamin, Inc.
Augenbaum, J.M. (1989). An adaptive pseudospectral method for discontinuous problems. Appl. Numer. Math. 5, 459–80
Axelsson, O. (1996). Iterative Solution Methods. Cambridge University Press.
Bagchi, P. and Balachandar, S. (2002a). Shear versus vortex-induced lift force on a rigid sphere at moderate Re. J. Fluid Mech. 473, 379–88
Bagchi, P. and Balachandar, S. (2002b). Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re. Phys. Fluids 14, 2719–37
Bagchi, P. and Balachandar, S. (2002c). Steady planar straining flow past a rigid sphere at moderate Reynolds number. J. Fluid Mech. 466, 365–407
Bagchi, P. and Balachandar, S. (2003). Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15(11), 3496–513
Bagchi, P. and Balachandar, S. (2004). Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123
Bai-Lin, H. (1984). Chaos. World Scientific Publishing Co.
Balachandar, S. and Eaton, J.K. (2010). Turbulent dispersed multiphase flow. Ann. Rev. Fluid Mech. 42, 111–33
Balachandar, S. and Maxey, M.R. (1989). Methods for evaluating fluid velocities in spectral simulations of turbulence. J. Comp. Phys. 83(1), 96–125
Ballal, B.Y. and Rivlin, R.S. (1976). Flow of a Newtonian fluid between eccentric rotating cylinders: inertial effects. Arch. Rational Mech. Anal. 62(3), 237–94
Barenblatt, G.I. (1996). Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics. Cambridge University Press.
Bashforth, F. and Adams, J.C. (1883). An Attempt to Test the Theories of Cap- illary Action: By Comparing the Theoretical and Measured Forms of Drops of Fluid. University Press.
Basset, A.B. (1888). A Treatise on Hydrodynamics. Deighton, Bell and Company.
Batchelor, G.K. (1967). An Introduction to Fluid Dynamics. Cambridge Univer- sity Press.
Ben-Jacob, E. and Garik, P. (1990). The formation of patterns in non-equilibrium growth. Nature 343, 523–30
Berry, M.V., Percival, I.C. and Weiss, N.O. (1987). Dynamical Chaos. The Royal Society, London. (First published as Proc. R. Soc. London A 413, 1–199)
Birkhoff, G. and Fisher, J. (1959). Do vortex sheets roll up? Rend. Circ. Mat. Palermo 8, 77–90
Boris, J.P. (1989). New directions in computational fluid dynamics. Ann. Rev. Fluid Mech. 21, 345–85
Boussinesq, J. (1885). Sur la résistance qu'oppose un liquide indéfini au repos au mouvement varié d'une sphére solide. C. R. Acad. Sci. Paris 100, 935–7
Boyd, J.P. (2001). Chebyshev and Fourier Spectral Methods. Courier Dover Publications.
Brachet, M.E., Meiron, D.I., Orszag, S.A., Nickel, B.G., Morf, R.H. and Frisch, U. (1983). Small scale structure of the Taylor–Green vortex. J. Fluid Mech. 130, 411–52
Brown, D.L., Cortez, R. and Minion, M.L. (2001). Accurate projection methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 168(2), 464– 99.
Brucato, A., Grisafi, F. and Montante, G. (1998). Particle drag coefficients in turbulent fluids. Chem. Eng. Sci. 53, 3295–314
Calhoun, D. and Leveque, R.J. (2000). A Cartesian grid finite-volume method for the advection–diffusion equation in irregular geometries. J. Comput. Phys. 157, 143–80
Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A. (2006). Spectral Methods in Fluid Dynamics. Springer.
Carnahan, B., Luther, H.A. and Wilkes, J.O. (1969). Applied Numerical Methods. Wiley.
Chaiken, J., Chevray, R., Tabor, M. and Tan, Q.M. (1986). Experimental study of Lagrangian turbulence in a Stokes flow. Proc. R. Soc. London A 408, 165–74
Chaiken, J., Chu, C.K., Tabor, M. and Tan, Q.M. (1987). Lagrangian turbulence and spatial complexity in a Stokes flow. Phys. Fluids 30, 687–94
Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Chang, E.J. and Maxey, M.R. (1994). Unsteady flow about a sphere at low to moderate Reynolds number. Part 1: Oscillatory motion. J. Fluid Mech. 277, 347–79
Chapra, S.C. (2002). Numerical Methods for Engineers, 4th edn. McGraw–Hill.
Chorin, A.J. (1968). Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745–62
Chorin, A.J. (1976). Random choice solution of hyperbolic systems. J. Comp. Phys. 22(4), 517–33
Chung, T.J. (2010). Computational Fluid Dynamics. Cambridge University Press.
Clift, R., Grace, J.R. and Weber, M.E. (1978). Bubbles, Drops and Particles. Academic Press.
Cochran, W.G. (1934). The flow due to a rotating disk. Proc. Camb. Phil. Soc. 30, 365–75
Collatz, L. (1960). The Numerical Treatment of Differential Equations. Springer.
Cossu, C. and Loiseleux, T. (1998). On the convective and absolute nature of instabilities in finite difference numerical simulations of open flows. J. Comp. Phys. 144(1), 98–108
Criminale, W.O., Jackson, T.L. and Joslin, R.D. (2003). Theory and Computa- tion of Hydrodynamic Stability. Cambridge University Press.
Crutchfield, J.P., Farmer, J.D., Packard, N.H. and Shaw, R.S. (1986). Chaos. Sci. Amer. 255, 46–57
Curle, N. (1957). On hydrodynamic stability in unlimited fields of viscous flow. Proc. Royal Soc. London A 238, 489–501
Curry, J.H., Garnett, L. and Sullivan, D. (1983). On the iteration of a rational function: computer experiments with Newton's method. Comm. Math. Phys. 91, 267–77
Curry, J.H., Herring, J.R., Loncaric, J. and Orszag, S.A. (1984). Order and disorder in two- and three-dimensional Benard convection. J. Fluid Mech. 147, 1–38
Dandy, D.S. and Dwyer, H.A. (1990). A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag and heat transfer. J. Fluid Mech. 216, 381–410
Devaney, R.L. (1989). An Introduction to Chaotic Dynamical Systems, 2nd edn. Addison–Wesley.
Deville, M.O., Fischer, P.F. and Mund, E.H. (2002). High-order Methods for Incompressible Fluid Flow. Cambridge University Press.
Dombre, T., Frisch, U., Greene, J.M., Hénon, M., Mehr, A. and Soward A.M. (1986). Chaotic streamlines and Lagrangian turbulence: the ABC flows. J. Fluid Mech. 167, 353–91
Dongarra, J.J., Croz, J.D., Hammarling, S. and Duff, I.S. (1990). A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Software (TOMS) 16(1), 1–17
Donnelly, R.J. (1991). Taylor–Couette flow: the early days. Phys. Today, Novem- ber, 32–9
Drazin, P.G. and Reid, W.H. (2004). Hydrodynamic Stability, 2nd edn. Cambridge University Press.
Eckhardt, B. and Aref, H. (1988). Integrable and chaotic motions of four vortices V. Collision dynamics of vortex pairs. Phil. Trans. Royal Soc. London A 326, 655–96
Edelsbrunner, H. (2001). Geometry and Topology for Mesh Generation. Cambridge University Press.
Eiseman, P.R. (1985). Grid generation for fluid mechanics computations. Ann. Rev. Fluid Mech. 17, 4875–22
Emmons, H.W. (1970). Critique of numerical modelling of fluid mechanics phe- nomena. Ann. Rev. Fluid Mech. 2, 15–37
Eswaran, V. and Pope, S.B. (1988). An examination of forcing in direct numerical simulations of turbulence. Comp. Fluid. 16(3), 257–78
Evans, G., Blackledge, J. and Yardley, P. (2012). Numerical Methods for Partial Differential Equations. Springer.
Fadlun, E.A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J. (2000). Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60
Fatou, P. (1919). Sur les equations fontionelles. Bull. Soc. Math. France 47, 161–271 also 48, 33–94 208–314
Feigenbaum, M.J. (1978). Quantitative universality for a class of non-linear transformations. J. Stat. Phys. 19, 25–52
Feigenbaum, M.J. (1980). The metric universal properties of period doubling bifurcations and the spectrum for a route to turbulence. Ann. N.Y. Acad. Sci. 357, 330–6
Ferziger, J.H. and Peric, M. (2012). Computational Methods for Fluid Dynamics. Springer.
Fink, P.T. and Soh, W.K. (1978). A new approach to roll-up calculations of vortex sheets. Proc. Royal Soc. London A 362, 195–209
Finlayson, B.A. and Scriven, L.E. (1966). The method of weighted residuals: a review. Appl. Mech. Rev. 19(9), 735–48
Finn, R. (1986). Equilibrium Capillary Surfaces. Springer.
Fischer, P.F., Leaf, G.K. and Restrepo, J.M. (2002). Forces on particles in oscil- latory boundary layers. J. Fluid Mech. 468, 327–47
Fjørtoft, R. (1950). Application of Integral Theorems in Deriving Criteria of Stability for Laminar Flows and for the Baroclinic Circular Vortex. Geofysiske Publikasjoner, Norske Videnskaps-Akademii Oslo.
Fletcher, C.A.J. (1991). Computational Techniques for Fluid Dynamics, Vol I and II. Springer.
Fornberg, B. (1988). Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471.
Fornberg, B. (1998). A Practical Guide to Pseudospectral Methods. Cambridge University Press.
Fox, R.O. (2012). Large-eddy-simulation tools for multiphase flows. Ann. Rev. Fluid Mech. 44, 47–76
Franceschini, V. and Tebaldi, C. (1979). Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier–Stokes equations. J. Stat. Phys. 21(6), 707–26
Funaro, D. (1992). Polynomial Approximation of Differential Equations. Springer.
Gatignol, R. (1983). The Faxén formulas for a rigid particle in an unsteady non-uniform Stokes-flow. J. Mécanique Théorique Appliquée 2(2), 143–60
Gear, C.W. (1971). Numerical Initial Value Problems in Ordinary Differential Equations. Prentice–Hall.
Ghia, U.K.N.G., Ghia, K.N. and Shin, C.T. (1982). High-Re solutions for incom- pressible flow using the Navier–Stokes equations and a multigrid method. J. Comp. Phys. 48(3), 387–411
Glendinning, P. (1994). Stability, Instability and Chaos: an Introduction to the Theory of Nonlinear Differential Equations. Cambridge University Press.
Glowinski, R. and Pironneau, O., (1992). Finite element methods for Navier– Stokes equations. Ann. Rev. Fluid Mech. 24, 167–204
Godunov, S.K. (1959). A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Math. Sbornik 47, 271–306 Translated as US Joint Publ. Res. Service, JPRS 7226 (1969).
Goldstein, D., Handler, R. and Sirovich, L. (1993). Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105, 354–66
Goldstine, H.H. (1972). The Computer from Pascal to Von Neumann. Princeton University Press.
Gollub, J.P. and Benson, S.V. (1980). Many routes to turbulent convection. J. Fluid Mech. 100, 449–70
Golub, G.H. (ed.) (1984). Studies in Numerical Analysis. The Mathematical Association of America.
Golub, G.H. and Kautsky, J. (1983). Calculation of Gauss quadratures with multiple free and fixed knots. Numerische Mathematik 41(2), 147–63
Golub, G.H. and van Loan, C.F. (2012). Matrix Computations. Johns Hopkins University Press.
Gore, R.A. and Crowe, C.T. (1990). Discussion of particle drag in a dilute tur- bulent two-phase suspension flow. Int. J. Multiphase Flow 16, 359–61
Gottlieb, D. and Orszag, S.A. (1983). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.
Guermond, J.L., Minev, P. and Shen, J. (2006). An overview of projection meth- ods for incompressible flows. Comp. Meth. Appl. Mech. Eng. 195(44), 6011–45
Gustafsson, B., Kreis, H.-O. and Sundstrøm, A. (1972). Stability theory of dif- ference approximations for mixed initial boundary value problems, II. Math. Comput. 26, 649–86
Hamming, R.W. (1973). Numerical Methods for Scientists: No-slip Engineers, 2nd edn. McGraw–Hill. (Republished by Dover Publications, 1986.)
Harrison, W.J. (1908). The influence of viscosity on the oscillations of superposed fluids. Proc. London Math. Soc. 6, 396–405
Hartland, S. and Hartley, R.W. (1976). Axisymmetric Fluid–Liquid Interfaces. Elsevier Scientific.
Hartree, D.R. (1937). On an equation occurring in Falkner and Skan's approxi- mate treatment of the equations of the boundary layer. Proc. Camb. Phil. Soc. 33, 223–39
Hénon, M. (1969). Numerical study of quadratic area-preserving mappings. Q. Appl. Math. 27, 291–312
Hénon, M. (1982). On the numerical computation of Poincaré maps. Physica D 5, 412–4
Higdon, J.J.L. (1985). Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities. J. Fluid Mech. 159, 195–226
Hildebrand, F.B. (1974). Introduction to Numerical Analysis, 2nd edn. McGraw– Hill. (Republished by Dover Publications).
Hirsch, C. (2007). Numerical Computation of Internal and External Flows: the Fundamentals of Computational Fluid Dynamics, 2nd edn. Butterworth– Heinemann.
Hirsch, M.W., Smale, S. and Devaney, R.L. (2004). Differential Equations, Dy- namical Systems, and an Introduction to Chaos. Academic Press.
Holt, M. (1977). Numerical Methods in Fluid Dynamics. Springer.
Howard, L.N. (1958). Hydrodynamic stability of a jet. J. Math. Phys. 37(1), 283–98
Huntley, H.E. (1967). Dimensional Analysis. Dover Publications.
Johnson, T.A. and Patel, V.C. (1999). Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70
Julia, G. (1918). Memoire sur l'iteration des fonctions rationelles. J. Math. Pures Appl. 4, 47–245
Kac, M. (1938). Sur les fonctions 2nt−[2nt]− 1. J. London Math. Soc. 13, 131–4
Kamath, V. and Prosperetti, A. (1989). Numerical integration methods in gas– bubble dynamics. J. Acoust. Soc. Amer. 85, 1538–48
Karniadakis, G.E. and Sherwin, S. (2013). Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press.
Karniadakis, G.E. and Triantafyllou, G.E. (1992). Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. J. Fluid Mech. 238, 1–30
Karniadakis, G.E., Israeli, M. and Orszag, S.A. (1991). High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–43
Keller, H.B. (1968). Numerical Methods for Two-point Boundary-value Problems. Dover Publications.
Kida, S. and Takaoka, M. (1987). Bridging in vortex reconnection. Phys. Fluids 30(10), 2911–4
Kim, D. and Choi, H. (2002). Laminar flow past a sphere rotating in the stream- wise direction. J. Fluid Mech. 461, 365–86
Kim, J. and Moin, P. (1985). Application of a fractional-step method to incom- pressible Navier–Stokes equations. J. Comp. Phys. 59, 308–23
Kim, I., Elghobashi, S. and Sirignano, W.A. (1998). Three-dimensional flow over 3-spheres placed side by side. J. Fluid Mech. 246, 465–88
Kim, J., Kim, D. and Choi, H. (2001). An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132–50
Kirchhoff, G.R. (1876). Vorlesungen Uber Mathematische Physik, Vol. 1. Teubner.
Knapp, R.T., Daily, J.W. and Hammitt, F.G. (1979). Cavitation. Institute for Hydraulic Research.
Knuth, D.E. (1981). The Art of Computer Programming, 2nd edn., Vol. 2. Addison–Wesley.
Kopal, Z. (1961). Numerical Analysis. Chapman and Hall.
Kozlov, V.V. and Onischenko, D.A. (1982). Nonintegrability of Kirchhoff's equa- tions. Sov. Math. Dokl. 26, 495–8
Krasny, R. (1986a). A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167, 65–93
Krasny, R. (1986b). Desingularization of periodic vortex sheet roll-up. J. Com- put. Phys. 65, 292–313
Kreiss, H.-O. and Oliger, J. (1972). Comparison of accurate methods for the integration of hyperbolic equations. Tellus 24(3), 199–215
Krishnan, G.P. and Leighton Jr, D.T. (1995). Inertial lift on a moving sphere in contact with a plane wall in a shear flow. Phys. Fluids 7(11), 2538–45
Kurose, R. and Komori, S. (1999). Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183–206
Lamb, Sir H. (1932). Hydrodynamics, 6th edn. Cambridge University Press.
Lanczos, C. (1938). Trigonometric interpolation of empirical and analytical func- tions. J. Math. Phys. 17, 123–99
Landau, L.D. and Lifshitz, E.M. (1987). Fluid Mechanics, 2nd edn. Pergamon Press.
Ledbetter, C.S. (1990). A historical perspective of scientific computing in Japan and the United States. Supercomputing Rev. 3(11), 31–7
Lee, H. and Balachandar, S. (2010). Drag and lift forces on a spherical particle moving on a wall in a shear flow at finite Re. J. Fluid Mech. 657, 89–125
Lee, H. and Balachandar, S. (2017). Effects of wall roughness on drag and lift forces of a particle at finite Reynolds number. Int. J. Multiphase Flow. 88, 116–132
Lee, H., Ha, M.Y. and Balachandar, S. (2011). Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re. Int. J. Multiphase Flow 37(2), 108–124
Legendre, D. and Magnaudet, J. (1998). The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech. 368, 81–126
Leighton, D. and Acrivos, A. (1985). The lift on a small sphere touching a plane in the presence of a simple shear flow. ZAMP 36(1), 174–8
Lele, S.K. (1992). Compact finite difference schemes with spectral-like resolution. J. Comp. Phys. 103(1), 16–42
Leonard, B.P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meth. Appl. Mech. Eng. 19(1), 59–98
LeVeque, R.J. (2007). Finite Difference Methods for Ordinary and Partial Dif- ferential Equations: Steady-state and Time-dependent Problems. SIAM.
LeVeque, R.J. and Li, Z. (1994). The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Nu- mer. Anal. 31, 1019.
Li, T.Y. and Yorke, J.A. (1975). Period three implies chaos. Amer. Math. Monthly 82, 985–92
Lighthill, M.J. (1978). Waves in Fluids. Cambridge University Press.
Lin, C.C. (1943). On the Motion of Vortices in Two Dimensions. University of Toronto Press.
Liseikin, V.D. (2009). Grid Generation Methods. Springer.
Lorenz, E.N. (1963). Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130– 41.
Luke, Y.L. (1969). The Special Functions and their Approximations. Academic Press.
Lundgren, T.S. and Pointin, Y.B. (1977). Statistical mechanics of two- dimensional vortices. J. Stat. Phys. 17, 323–55
MacCormack, R.W. (1969). The effect of viscosity in hypervelocity impact cra- tering. AIAA Paper 69–354
MacCormack, R.W. and Lomax, H. (1979). Numerical solution of compressible viscous flows. Ann. Rev. Fluid Mech. 11, 289–316
Mack, L.M. (1976). A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73(3), 497–520
MacKay, R.S. and Meiss, J.D. (1987). Hamiltonian Dynamical Systems: A Reprint Selection. Adam Hilger.
Maeder, R.E. (1995). Function iteration and chaos. Math. J. 5, 28–40
Magnaudet, J., Rivero, M. and Fabre, J. (1995). Accelerated flows past a rigid sphere or a spherical bubble. Part 1: Steady straining flow. J. Fluid Mech. 284, 97–135
Mandelbrot, B.B. (1980). Fractal aspects of z → Λz(1 − z) for complex Λ and z. Ann. N.Y. Acad. Sci. 357, 249–59
Mandelbrot, B.B. (1983). The Fractal Geometry of Nature. Freeman.
Marella, S., Krishnan, S.L.H.H., Liu, H. and Udaykumar, H.S. (2005). Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving boundary computations. J. Comp. Phys. 210(1), 1–31
Matsuda, K., Onishi, R., Hirahara, M., Kurose, R., Takahashi, K. and Komori, S. (2014). Influence of microscale turbulent droplet clustering on radar cloud observations. J. Atmos. Sci. 71(10), 3569–82
Maxey, M.R. and Riley, J.J. (1983). Equation of motion for a small rigid sphere in a non-uniform flow. Phys. Fluids 26(4), 883–9
May, R.M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459–67
McLaughlin, J.B. (1991). Inertial migration of a small sphere in linear shear flows. J. Fluid Mech. 224, 261–74
McQueen, D.M. and Peskin, C.S. (1989). A three-dimensional computational method for blood flow in the heart. II. Contractile fibers. J. Comput. Phys. 82, 289.
Mei, R. and Adrian, R.J. (1992). Flow past a sphere with an oscillation in the free-stream and unsteady drag at finite Reynolds number. J. Fluid Mech. 237, 133–74
Meiron, D.I., Baker, G.R. and Orszag, S.A. (1982). Analytic structure of vortex sheet dynamics 1. Kelvin–Helmholtz instability. J. Fluid Mech. 114, 283–98
Mercier, B. (1989). An Introduction to the Numerical Analysis of Spectral Meth- ods. Springer.
Merilees, P.E. (1973). The pseudospectral approximation applied to the shallow water equations on a sphere. Atmosphere 11(1), 13–20
Mitchell, A.R. and Griffiths, D.F. (1980). The Finite Difference Method in Partial Differential Equations. John Wiley.
Mittal, R. (1999). A Fourier–Chebyshev spectral collocation method for simulat- ing flow past spheres and spheroids. Int. J. Numer. Meth. Fluids 30, 921–37
Mittal, R. and Balachandar, S. (1996). Direct numerical simulations of flow past elliptic cylinders. J. Comput. Phys. 124, 351–67
Mittal, R. and Iaccarino, G. (2005). Immersed boundary methods. Ann. Rev. Fluid Mech. 37, 239–61
Mohd-Yusof, J. (1997). Combined immersed boundaries B-spline methods for simulations of flows in complex geometries. CTR Annual Research Briefs. NASA Ames, Stanford University.
Moin, P. (2010a). Fundamentals of Engineering Numerical Analysis. Cambridge University Press.
Moin, P. (2010b). Engineering Numerical Analysis. Cambridge University Press.
Moin, P. and Krishnan, M. (1998). Direct numerical simulation: a tool in turbu- lence research. Ann. Rev. Fluid Mech. 30(1), 539–78
Moore, D.W. (1979). The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. Royal Soc. London A 365, 105–19
Morton, K.W. (1980). Stability of finite difference approximations to a diffusion– convection equation. Int. J. Numer. Method. Eng. 15(5), 677–83
Moser, J. (1973). Stable and Random Motions in Dynamical Systems. Ann. Math. Studies No.77. Princeton University Press.
Onsager, L. (1949). Statistical hydrodynamics. Nuovo Cim. 6 (Suppl.), 279–87
Orszag, S.A. (1969). Numerical methods for the simulation of turbulence. Phys. Fluids 12(12), Supp. II, 250–7
Orszag, S.A. (1970). Transform method for the calculation of vector-coupled sums: application to the spectral form of the vorticity equation. J. Atmos. Sci. 27(6), 890–5
Orszag, S.A. (1974). Fourier series on spheres. Monthly Weather Rev. 102(1), 56–75
Orszag, S.A. and Israeli, M. (1974). Numerical simulation of viscous incompress- ible flows. Ann. Rev. Fluid Mech. 6, 281–318
Orszag, S.A. and McLaughlin, N.N. (1980). Evidence that random behavior is generic for nonlinear differential equations. Physica D 1, 68–79
Orszag, S.A. and Patterson Jr, G.S. (1972). Numerical simulation of three- dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28(2), 76.
Orszag, S.A., Israeli, M. and Deville, M. (1986). Boundary conditions for incom- pressible flows. J. Sci. Comput. 1, 75–111
Oseen, C.W. (1927). Hydrodynamik. Akademische Verlagsgesellschaft.
Ottino, J.M. (1989). The Kinematics of Mixing: Stretching, Chaos and Trans- port. Cambridge University Press.
Patterson, G. (1978). Prospects for computational fluid mechanics. Ann. Rev. Fluid Mech. 10, 289–300
Peaceman, D.W. and Rachford Jr, H.H. (1955). The numerical solution of parabolic and elliptic differential equations. J. Soc. Indus. Appl. Math. 3(1), 28–41
Peitgen, H.-O. and Richter, P.H. (1986). The Beauty of Fractals. Springer.
Peitgen, H.-O. and Saupe, D. (eds.) (1988). The Science of Fractal Images. Springer.
Peitgen, H.-O., Saupe, D. and Haessler, F.V. (1984). Cayley's problem and Julia sets. Math. Intelligencer 6, 11–20
Pember, R.B., Bell, J.B., Colella, P., Crutchfield, W.Y. and Welcome, M.L. (1995). An adaptive Cartesian grid method for unsteady compressible flow in irregular regions. J. Comput. Phys. 120, 278–304
Perot, J.B. (1993). An analysis of the fraction step method. J. Comput. Phys. 108, 51–8
Peskin, C.S. (1977). Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220–52
Peyret, R. and Taylor, T.D. (1983). Computational Methods for Fluid Flow. Springer.
Pinelli, A., Naqavi, I.Z., Piomelli, U. and Favier, J. (2010). Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers. J. Comp. Phys. 229(24), 9073–91
Pirozzoli, S. (2011). Numerical methods for high-speed flows. Ann. Rev. Fluid Mech. 43, 163–94
Plesset, M.S. and Prosperetti, A. (1977). Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 145–85
Pletcher, R.H., Tannehill, J.C. and Anderson, D. (2012). Computational Fluid Mechanics and Heat Transfer. CRC Press.
Pozrikidis, C. (2011). Introduction to Theoretical and Computational Fluid Dy- namics. Oxford University Press.
Pozrikidis, C. and Higdon, J.J.L. (1985). Nonlinear Kelvin–Helmholtz instability of a finite vortex layer. J. Fluid Mech. 157, 225–63
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1986). Nu- merical Recipes: The Art of Scientific Programming. Cambridge University Press.
Prosperetti, A. and Tryggvason, G. (eds.) (2009). Computational Methods for Multiphase Flow. Cambridge University Press.
Proudman, I. and Pearson, J.R.A. (1957). Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2(3), 237–62
Rayleigh, Lord (1880). On the stability, or instability, of certain fluid motions. Proc. London Math. Soc. 11, 57–72
Rice, J.R. (1983). Numerical Methods, Software, and Analysis, IMSL Reference Edition. McGraw–Hill.
Richtmyer, R.D., and Morton, K.W. (1994). Difference Methods for Initial-Value Problems, 2nd edn. Krieger Publishing Co.
Roache, P.J. (1976). Computational Fluid Dynamics. Hermosa.
Roberts, K.V. and Christiansen, J.P. (1972). Topics in computational fluid mechanics. Comput. Phys. Comm. 3(Suppl.), 14–32
Roe, P.L. (1986). Characteristic-based schemes for the Euler equations. Ann. Rev. Fluid Mech. 18, 337–65
Roma, A.M., Peskin, C.S. and Berger, M.J. (1999). An adaptive version of the immersed boundary method. J. Comp. Phys. 153(2), 509–34
Rosenblum, L.J. (1995). Scientific visualization: advances and challenges. IEEE Comp. Sci. Eng. 2(4), 85.
Rosenhead, L. (1931). The formation of vortices from a surface of discontinuity. Proc. Roy. Soc. London Ser. A 134, 170–92
Rosenhead, L. (ed.) (1963). Laminar Boundary Layers. Oxford University Press.
Rudoff, R.C. and Bachalo, W.D. (1988) Measurement of droplet drag coefficients in polydispersed turbulent flow fields. AIAA Paper, 88–0235
Saad, Y. (2003). Iterative Methods for Sparse Linear Systems. SIAM.
Saff, E.B. and Kuijlaars, A.B. (1997). Distributing many points on a sphere. Math. Intelligencer 19(1), 5–11
Saffman, P.G. (1965). The lift on a small sphere in a slow shear flow. J. Fluid Mech.. 22, 385–400
Saiki, E.M. and Biringen, S. (1996). Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method. J. Comput. Phys. 123, 450–65
Sankagiri, S. and Ruff, G.A. (1997). Measurement of sphere drag in high turbu- lent intensity flows. Proc. ASME FED. 244, 277–82
Sansone, G. (1959). Orthogonal Functions. Courier Dover Publications.
Sato, H. and Kuriki, K. (1961). The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11(3), 321–52
Schlichting, H. (1968). Boundary-Layer Theory. McGraw–Hill.
Shampine, L.F. and Gordon, M.K. (1975). Computer Solution of Ordinary Dif- ferential Equations. W.H. Freeman and Co.
Shirayama, S. (1992). Flow past a sphere: topological transitions of the vorticity field. AIAA J. 30, 349–58
Shu, S.S. (1952). Note on the collapse of a spherical cavity in a viscous, incom- pressible fluid. In Proc. First US Nat. Congr. Appl. Mech. ASME, pp. 823–5
Siemieniuch, J.L. and I., Gladwell. (1978). Analysis of explicit difference methods for a diffusion–convection equation. Int. J. Numer. Method. Eng. 12(6), 899– 916.
Silcock, G. (1975). On the Stability of Parallel Stratified Shear Flows. PhD Dis- sertation, University of Bristol.
Smereka, P., Birnir, B. and Banerjee, S. (1987). Regular and chaotic bubble oscillations in periodically driven pressure fields. Phys. Fluids 30, 3342–50
Smith, G.D. (1985). Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Press.
Sommerfeld, A. (1964). Mechanics of Deformable Bodies. Academic Press
Spalart, P.R. (2009). Detached-eddy simulation. Ann. Rev. Fluid Mech. 41, 181– 202.
Squire, H.B. (1933). On the stability for three-dimensional disturbances of vis- cous fluid flow between parallel walls. Proc. Roy. Soc. London A 142, 621–8
Stewartson, K. (1954). Further solutions of the Falkner–Skan equation. Math. Proc. Cambridge Phil. Soc. 50(3), 454–65
Strang, G. (2016). Introduction to Linear Algebra, 5th edn. Wellesley-Cambridge Publishers.
Streett, C.L. and Macaraeg, M. (1989). Spectral multi-domain for large-scale fluid dynamics simulations. Appl. Numer. Math. 6, 123–39
Struik, D.J. (1961). Lectures on Classical Differential Geometry, 2nd edn. Addison–Wesley. (Reprinted by Dover Publications, 1988.)
Swanson, P.D. and Ottino, J.M. (1990). A comparative computational and exper- imental study of chaotic mixing of viscous fluids. J. Fluid Mech. 213, 227–49
Taneda, S. (1963). The stability of two-dimensional laminar wakes at low Reynolds numbers. J. Phys. Soc. Japan 18(2), 288–96
Temam, R. (1969). Sur l'approximation de la solution des équations de Navier– Stokes par la méthode des pas fractionnaires (II). Arch. Ration. Mech. Anal. 33, 377–85
Tennetti, S., Garg, R. and Subramaniam, S. (2011). Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. Int. J. Multiphase Flow 37(9), 1072–92
Theofilis, V. (2011). Global linear instability. Ann. Rev. Fluid Mech. 43, 319–52
Thomas, J.W. (2013). Numerical Partial Differential Equations: Finite Differ- ence Methods. Springer.
Thompson, J.F., Warsi, Z.U.A. and Mastin, C.W. (1982). Boundary-fitted co- ordinate systems for numerical solution of partial differential equations – a review. J. Comp. Phys. 47, 1–108
Thompson, J.F., Warsi, Z.U.A. and Mastin, C.W. (1985). Numerical Grid Generation. North–Holland.
Tomboulides, A.G. and Orszag, S.A. (2000). Numerical investigation of transi- tional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73
Toro, E.F. (1999). Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer.
Trefethen, L.N. (1982). Group velocity in finite difference schemes. SIAM Rev. 24(2), 113–36
Trefethen, L.N. and Embree, M. (2005). Spectra and Pseudospectra: The Behav- ior of Non-normal Matrices and Operators. Princeton University Press.
Tseng, Y.-H. and Ferziger, J.H. (2003). A ghost-cell immersed boundary method for flow in complex geometry. J. Comp. Phys. 192(2), 593–623
Udaykumar, H.S., Kan, H.-C., Shyy, W. and Tran-son-Tay, R. (1997). Multiphase dynamics in arbitrary geometries on fixed Cartesian grids. J. Comput. Phys. 137, 366–405
Udaykumar, H.S., Mittal, R. and Shyy, W. (1999). Solid–fluid phase front com- putations in the sharp interface limit on fixed grids. J. Comput. Phys. 153, 535–74
Udaykumar, H.S., Mittal, R., Rampunggoon, P. and Khanna, A. (2001). A sharp interface Cartesian grid method for simulating flows with complex moving boundaries. J. Comput. Phys. 174, 345–80
Uhlherr, P.H.T. and Sinclair, C.G. (1970). The effect of freestream turbulence on the drag coefficients of spheres. Proc. Chemca. 1, 1–12
Uhlmann, M. (2005). An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comp. Phys. 209(2), 448–76
Uhlmann, M. and Doychev, T. (2014). Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech. 752, 310–48
Ulam, S.M. and von Neumann, J. (1947). On combinations of stochastic and deterministic processes. Bull. Amer. Math. Soc. 53, 1120.
van de Vooren, A.I. (1980). A numerical investigation of the rolling-up of vortex sheets. Proc. Roy. Soc. London A. 373, 67–91
van Dyke, M. (1964). Perturbation Methods in Fluid Mechanics. Academic Press.
van Dyke, M. (1982). An Album of Fluid Motion. Parabolic Press.
van Dyke, M. (1994). Computer-extended series. Ann. Rev. Fluid Mech. 16(1), 287–309
van Kan, J. (1986). A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7(3), 870–91
van Leer, B. (1974). Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme. J. Comp. Phys. 14(4), 361–70
Varga, R.S. (1962). Matrix Iterative Methods. Prentice–Hall Inc.
Versteeg, H.K. and Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson Education.
Vrscay, E.R. (1986). Julia sets and Mandelbrot-like sets associated with higher- order Schröder rational iteration functions: a computer assisted study. Math. Comp. 46, 151–69
Wang, M., Freund, J.B. and Lele, S.K. (2006). Computational prediction of flow- generated sound. Ann. Rev. Fluid Mech. 38, 483–512
Warnica, W.D., Renksizbulut, M. and Strong, A.B. (1994). Drag coefficient of spherical liquid droplets. Exp. Fluids 18, 265–70
Wazzan, A.R., Okamura, T. and Smith, A.M.O. (1968). The stability of water flow over heated and cooled flat plates. J. Heat Transfer 90(1), 109–14
Wendroff, B. (1969). First Principles of Numerical Analysis: An Undergraduate Text. Addison–Wesley.
White, F.M. (1974). Viscous Flow Theory. McGraw–Hill.
Whittaker, E.T. (1937). A Treatise on the Analytical Mechanics of Particles and Rigid Bodies, 4th edn. Cambridge University Press.
Wilkinson, J.H. (1965). The Algebraic Eigenvalue Problem. Clarendon Press.
Yakhot, V., Bayly, B. and Orszag, S.A. (1986). Analogy between hyperscale transport and cellular automaton fluid dynamics. Phys. Fluids 29, 2025–7
Ye, T., Mittal, R., Udaykumar, H.S. and Shyy, W. (1999). An accurate Cartesian grid method for viscous incompressible flows with complex immersed bound- aries. J. Comput. Phys. 156, 209–40
Yee, S.Y. (1981). Solution of Poisson's equation on a sphere by truncated double Fourier series. Monthly Weather Rev. 109(3), 501–5
Yeung, P.K. and Pope, S.B. (1988). An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comp. Phys. 79(2), 373–416
Young, D.M. (2014). Iterative Solution of Large Linear Systems. Elsevier.
Young, D.M. and Gregory, R.T. (1988). A Survey of Numerical Mathematics, Vols. I and II. Dover Publications.
Zabusky, N.J. (1987). A numerical laboratory. Phys. Today 40, 28–37
Zabusky, N.J. and Kruskal, M.D. (1965). Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15(6), 240.
Zabusky, N.J. and Melander, M.V. (1989). Three-dimensional vortex tube recon- nection: morphology for orthogonally-offset tubes. Physica D 37, 555–62
Zarin, N.A. and Nicholls, J.A. (1971). Sphere drag in solid rockets – non- continuum and turbulence effects. Comb. Sci. Tech. 3, 273–80
Zeng, L., Najjar, F., Balachandar, S. and Fischer, P. (2009). Forces on a finite- sized particle located close to a wall in a linear shear flow. Phys. Fluids 21(3), 033302.
Zhang, L., Gerstenberger, A., Wang, X. and Liu, W.K. (2004). Immersed finite element method. Comp. Meth. Appl. Mech. Eng. 193(21), 2051–67