References
- Abkar16
- Mahdi Abkar , Hyun J. Bae , Parviz Moin (2016), Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows, Physical Review Fluids, 1(4), 2016.
- Abkar17
- Mahdi Abkar , Parviz Moin (2017), Large- { Eddy } { Simulation } of { Thermally } { Stratified } { Atmospheric } { Boundary } - { Layer } { Flow } { Using } a { Minimum } { Dissipation } { Model }, Boundary-Layer Meteorology, 165(3), 405--419, 2017.
- Arakawa77
- Akio Arakawa , Vivian R. Lamb (1977), Computational { Design } of the { Basic } { Dynamical } { Processes } of the { UCLA } { General } { Circulation } { Model }, In , editors, Methods in { Computational } { Physics } : { Advances } in { Research } and { Applications }, 173--265. Elsevier, 1977.
- Ascher95
- U. Ascher , S. Ruuth , B. Wetton (1995), Implicit- { Explicit } { Methods } for { Time } - { Dependent } { Partial } { Differential } { Equations }, SIAM Journal on Numerical Analysis, 32(3), 797--823, 1995.
- Batchelor00
- G. K. Batchelor (2000), { An Introduction to Fluid Dynamics }, Cambridge University Press, 2000.
- Besard16
- Tim Besard , Pieter Verstraete , Bjorn De Sutter (2016), High-level { GPU } programming in { Julia }, arXiv:1604.03410 [cs], 0, 2016.
- Besard19GPU
- Tim Besard , Christophe Foket , Bjorn De Sutter (2019), Effective { Extensible } { Programming } : { Unleashing } { Julia } on { GPUs }, IEEE Transactions on Parallel and Distributed Systems, 30(4), 827--841, 2019.
- Besard19Prototype
- Tim Besard , Valentin Churavy , Alan Edelman , Bjorn De Sutter (2019), Rapid software prototyping for heterogeneous and distributed platforms, Advances in Engineering Software, 132, 29--46, 2019.
- Bezanson17
- Jeff Bezanson , Alan Edelman , Stefan Karpinski , Viral B. Shah (2017), Julia: { A } { Fresh } { Approach } to { Numerical } { Computing }, SIAM Review, 59, 65--98, 2017.
- Bianco99
- F. Bianco , G. Puppo , G. Russo (1999), High- { Order } { Central } { Schemes } for { Hyperbolic } { Systems } of { Conservation } { Laws }, SIAM Journal on Scientific Computing, 21, 294--322, 1999.
- Botella98
- O. Botella , R. Peyret (1998), Benchmark spectral results on the lid-driven cavity flow, Computers \& Fluids, 27(4), 421--433, 1998.
- Boussinesq1877
- J. Boussinesq (1877), Essai sur la th { \'e } orie des eaux courantes, Impr. Nationale, 1877.
- Boussinesq1903
- Joseph Boussinesq (1903), Th { \ = o } rie analytique de la chaleur, Gauthier-Villars, Tome , Paris, 1903.
- Brown01
- David L. Brown , Ricardo Cortez , Michael L. Minion (2001), Accurate { Projection } { Methods } for the { Incompressible } { Navier } – { Stokes } { Equations }, Journal of Computational Physics, 168(2), 464--499, 2001.
- Bruneau06
- Charles-Henri Bruneau , Mazen Saad (2006), The 2D lid-driven cavity problem revisited, Computers \& Fluids, 35(3), 326--348, 2006.
- Burggraf66
- Odus R. Burggraf (1966), Analytical and numerical studies of the structure of steady separated flows, Journal of Fluid Mechanics, 24, 113--151, 1966.
- Buzbee70
- B. Buzbee , G. Golub , C. Nielson (1970), On { Direct } { Methods } for { Solving } { Poisson } ’s { Equations }, SIAM Journal on Numerical Analysis, 7(4), 627--656, 1970.
- Chaplygin1903
- S. A. Chaplygin (1903), One case of vortex motion in fluid, Trans. Phys. Sect. Imperial Moscow Soc. Friends of Natural Sciences, 11(2), 11--14, 1903.
- Chou45
- P. Y. Chou (1945), On velocity correlations and the solutions of the equations of turbulent fluctuation, Quarterly of Applied Mathematics, 3, 38--54, 1945.
- Corrsin61
- S. Corrsin (1961), Turbulent flow, American Scientist, 49(3), 300--325, 1961.
- Deardorff70
- J. W. Deardorff (1970), A numerical study of three-dimensional turbulent channel flow at large { Reynolds } numbers, Journal of Fluid Mechanics, 41(2), 453--480, 1970.
- Deardorff74
- J. W. Deardorff (1974), Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer, Boundary-Layer Meteorology, 7, 81--106, 1974.
- Deusebio15
- Enrico Deusebio , C. P. Caulfield , J. R. Taylor (2015), The intermittency boundary in stratified plane { Couette } flow, Journal of Fluid Mechanics, 781, 298--329, 2015.
- Erturk05
- E. Erturk , T. C. Corke , C. Gökçöl (2005), Numerical solutions of 2- { D } steady incompressible driven cavity flow at high { Reynolds } numbers, International Journal for Numerical Methods in Fluids, 48(7), 747--774, 2005.
- Flierl83
- Glenn R. Flierl , Melvin E. Stern , John A. Whitehead (1983), The physical significance of modons: { Laboratory } experiments and general integral constraints, Dynamics of Atmospheres and Oceans, 7(4), 233--263, 1983.
- Flierl87
- G R Flierl (1987), Isolated { Eddy } { Models } in { Geophysics }, Annual Review of Fluid Mechanics, 19, 493--530, 1987.
- Frigo05
- M. Frigo , S.G. Johnson (2005), The { Design } and { Implementation } of { FFTW } 3, Proceedings of the IEEE, 93(2), 216--231, 2005.
- Frigo98
- M. Frigo , S.G. Johnson (1998), { FFTW } : an adaptive software architecture for the { FFT }, In Proceedings of the 1998 { IEEE } { International } { Conference } on { Acoustics } , { Speech } and { Signal } { Processing } , { ICASSP } '98 ( { Cat } . { No } .98CH36181), 1381--1384, Seattle , WA , USA, 1998. IEEE.
- Ghia82
- U Ghia , K.N Ghia , C.T Shin (1982), High- { Re } solutions for incompressible flow using the { Navier } - { Stokes } equations and a multigrid method, Journal of Computational Physics, 48(3), 387--411, 1982.
- Harlow65
- Francis H. Harlow , J. Eddie Welch (1965), Numerical { Calculation } of { Time } - { Dependent } { Viscous } { Incompressible } { Flow } of { Fluid } with { Free } { Surface }, Physics of Fluids, 8(12), 2182--89, 1965.
- Hesthaven07
- Jan S Hesthaven , Tim Warburton (2007), { Nodal discontinuous Galerkin methods: algorithms , analysis , and applications }, Springer Science \& Business Media, 2007.
- Hill1894
- Micaiah John Muller Hill (1894), On a { Spherical } { Vortex }, Philosophical Transactions of the Royal Society A: Mathematical , Physical and Engineering Sciences, 185, 213--245, 1894.
- Hockney65
- R. W. Hockney (1965), A { Fast } { Direct } { Solution } of { Poisson } 's { Equation } { Using } { Fourier } { Analysis }, Journal of the ACM, 12, 95--113, 1965.
- Hockney69
- R. W. Hockney (1969), The potential calculation and some applications, In B. Adler , S. Fernback , M. Rotenberg , editors, Methods of Computational Physics, 136--211. Academic Press, New York and London, 1969.
- Innes19
- Mike Innes , Alan Edelman , Keno Fischer , Chris Rackauckas , Elliot Saba , Viral B. Shah , Will Tebbutt (2019), A { Differentiable } { Programming } { System } to { Bridge } { Machine } { Learning } and { Scientific } { Computing }, arXiv:1907.07587 [cs], 0, 2019.
- Jiang96
- Guang-Shan Jiang , Chi-Wang Shu (1996), Efficient { Implementation } of { Weighted } { ENO } { Schemes }, Journal of Computational Physics, 126, 202--228, 1996.
- Kato69
- H. Kato , O. M. Phillips (1969), On the penetration of a turbulent layer into stratified fluid, Journal of Fluid Mechanics, 37(4), 643--655, 1969.
- Kerr96
- Robert M. Kerr (1996), Rayleigh number scaling in numerical convection, Journal of Fluid Mechanics, 310, 139--179, 1996.
- Kolmogorov41
- A. Kolmogorov (1941), { The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds' Numbers }, C. R. Akademiia U.R.S.S. (Doklady), 30, 301--305, 1941.
- Kumar16
- N. Kumar , J.H.M. Boonkkamp , B. Koren (2016), Local BVP methods for the computation of cell-face velocities in the incompressible Navier-Stokes equations, Technische Universiteit Eindhoven, 2016.
- Kundu15
- Pijush K. Kundu , Ira M. Cohen , David R Dowling (2015), { Fluid Mechanics }, Academic Press, 2015.
- Lamb45
- Horace Lamb (1945), Hydrodynamics, Dover Publications, 1945.
- Landau87
- L. D. Landau , E. M. Lifshitz (1987), { Fluid Mechanics: Volume 6 (Course of Theoretical Physics) }, Butterworth-Heinemann, 1987.
- Leonard75
- A. Leonard (1975), Energy { Cascade } in { Large } - { Eddy } { Simulations } of { Turbulent } { Fluid } { Flows }, In , editors, Advances in { Geophysics }, 237--248. Elsevier, 1975.
- Levy99
- Doron Levy , Gabriella Puppo , Giovanni Russo (1999), Central { WENO } schemes for hyperbolic systems of conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, 33(3), 547--571, 1999.
- Lilly66
- D K Lilly (1966), The { Representation } of { Small } - { Scale } { Turbulence } in { Numerical } { Simulation } { Experiments } ., NCAR Manuscript No. 281, 0, 1966.
- Liu94
- Xu-Dong Liu , Stanley Osher , Tony Chan (1994), Weighted { Essentially } { Non } -oscillatory { Schemes }, Journal of Computational Physics, 115, 200--212, 1994.
- Makhoul80
- J. Makhoul (1980), A fast cosine transform in one and two dimensions, IEEE Transactions on Acoustics , Speech , and Signal Processing, 28, 27--34, 1980.
- Marshall97FV
- John Marshall , Alistair Adcroft , Chris Hill , Lev Perelman , Curt Heisey (1997), A finite-volume , incompressible { Navier } { Stokes } model for studies of the ocean on parallel computers, Journal of Geophysical Research: Oceans, 102(C3), 5753--5766, 1997.
- Marshall97HY
- John Marshall , Chris Hill , Lev Perelman , Alistair Adcroft (1997), Hydrostatic , quasi-hydrostatic , and nonhydrostatic ocean modeling, Journal of Geophysical Research: Oceans, 102(C3), 5733--5752, 1997.
- Meleshko94
- V.V. Meleshko , G.J.F.van Heijst (1994), On { Chaplygin } 's investigations of two-dimensional vortex structures in an inviscid fluid, Journal of Fluid Mechanics, 272, 157--182, 1994.
- Oberbeck1879
- A. Oberbeck (1879), { Über die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge vor Temperaturdifferenzen }, Annalen der Physik, 243(6), 271--292, 1879.
- Orszag86
- Steven A. Orszag , Moshe Israeli , Michel O. Deville (1986), Boundary conditions for incompressible flows, Journal of Scientific Computing, 1(1), 75--111, 1986.
- Patankar80
- Suhas Patankar (1980), { Numerical Heat Transfer and Fluid Flow }, CRC Press, 1980.
- Pope00
- S. B. Pope (2000), Turbulent flows, Cambridge University Press, 2000.
- Pope04
- Stephen B Pope (2004), Ten questions concerning the large-eddy simulation of turbulent flows, New Journal of Physics, 6, 35--35, 2004.
- Pressel15
- Kyle G. Pressel , Colleen M. Kaul , Tapio Schneider , Zhihong Tan , Siddhartha Mishra (2015), Large-eddy simulation in an anelastic framework with closed water and entropy balances, Journal of Advances in Modeling Earth Systems, 7(3), 1425--1456, 2015.
- Revels18
- Jarrett Revels , Tim Besard , Valentin Churavy , Bjorn De Sutter , Juan Pablo Vielma (2018), Dynamic { Automatic } { Differentiation } of { GPU } { Broadcast } { Kernels }, arXiv:1810.08297 [cs], 0, 2018.
- Reynolds1895
- Osborne Reynolds (1895), On the dynamical theory of incompressible viscous fluids and the determination of the criterion, Philosophical Transactions of the Royal Society of London A, 186, 123--164, 1895.
- Roquet15Idealized
- Fabien Roquet , Gurvan Madec , Laurent Brodeau , J. Nycander (2015), Defining a { Simplified } { Yet } “ { Realistic } ” { Equation } of { State } for { Seawater }, Journal of Physical Oceanography, 45(10), 2564--2579, 2015.
- Roquet15TEOS
- F. Roquet , G. Madec , Trevor J. McDougall , Paul M. Barker (2015), Accurate polynomial expressions for the density and specific volume of seawater using the { TEOS } -10 standard, Ocean Modelling, 90, 29--43, 2015.
- Rozema15
- Wybe Rozema , Hyun J. Bae , Parviz Moin , Roel Verstappen (2015), Minimum-dissipation models for large-eddy simulation, Physics of Fluids, 27(8), 085107, 2015.
- Sani81
- R. L. Sani , P. M. Gresho , R. L. Lee , D. F. Griffiths (1981), The cause and cure (?) of the spurious pressures generated by certain { FEM } solutions of the incompressible { Navier } - { Stokes } equations: { Part } 1, International Journal for Numerical Methods in Fluids, 1(1), 17--43, 1981.
- Scase18
- M. M. Scase , H. L. Terry (2018), Spherical vortices in rotating fluids, Journal of Fluid Mechanics, 846, R4, 2018.
- Schroeder06
- Guido Schroeder , K. Heinke Schlünzen , Frank Schimmel (2006), Use of (weighted) essentially non-oscillatory advection schemes in a mesoscale model, Quarterly Journal of the Royal Meteorological Society, 132(618), 1509--1526, 2006.
- Schumann88
- Ulrich Schumann , Roland A Sweet (1988), Fast { Fourier } transforms for direct solution of poisson's equation with staggered boundary conditions, Journal of Computational Physics, 75, 123--137, 1988.
- Shu09
- Chi-Wang Shu (2009), High { Order } { Weighted } { Essentially } { Nonoscillatory } { Schemes } for { Convection } { Dominated } { Problems }, SIAM Review, 51, 82--126, 2009.
- Shu98
- Chi-Wang Shu (1998), Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, In Alfio Quarteroni , editors, Advanced { Numerical } { Approximation } of { Nonlinear } { Hyperbolic } { Equations }, 325--432. Springer Berlin Heidelberg, Berlin , Heidelberg, 1998.
- Smagorinsky63
- J. Smagorinsky (1963), General circulation experiments with the primitive equations { I } . { The } basic experiment, Monthly Weather Review, 91(3), 99--164, 1963.
- Sod78
- Gary A Sod (1978), A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of Computational Physics, 27, 1--31, 1978.
- Swarztrauber77
- Paul N. Swarztrauber (1977), The { Methods } of { Cyclic } { Reduction } , { Fourier } { Analysis } and the { FACR } { Algorithm } for the { Discrete } { Solution } of { Poisson } ’s { Equation } on a { Rectangle }, SIAM Review, 19(3), 490--501, 1977.
- Taylor22
- Geoffrey Ingram Taylor (1922), The motion of a sphere in a rotating liquid, Proceedings of the Royal Society of London. Series A , Containing Papers of a Mathematical and Physical Character, 102(715), 180--189, 1922.
- Taylor37
- Geoffrey Ingram Taylor , Albert Edward Green (1937), Mechanism of the production of small eddies from large ones, Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 158(895), 499--521, 1937.
- Temperton79
- Clive Temperton (1979), Direct methods for the solution of the discrete { Poisson } equation: { Some } comparisons, Journal of Computational Physics, 31, 1--20, 1979.
- Temperton80
- Clive Temperton (1980), On the { FACR } $(\ell)$ algorithm for the discrete { Poisson } equation, Journal of Computational Physics, 34(3), 314--329, 1980.
- Vallis17
- Geoffrey K Vallis (2017), Atmospheric { and } { Oceanic } { Fluid } { Dynamics }, Cambridge University Press, 2017.
- Verstappen18
- Roel Verstappen (2018), How much eddy dissipation is needed to counterbalance the nonlinear production of small , unresolved scales in a large-eddy simulation of turbulence?, Computers \& Fluids, 176, 276--284, 2018.
- Vreugdenhil18
- Catherine A. Vreugdenhil , John R. Taylor (2018), Large-eddy simulations of stratified plane { Couette } flow using the anisotropic minimum-dissipation model, Physics of Fluids, 30(8), 085104, 2018.
- White05
- A. A. White , B. J. Hoskins , I. Roulstone , A. Staniforth (2005), Consistent approximate models of the global atmosphere: shallow , deep , hydrostatic , quasi-hydrostatic and non-hydrostatic, Quarterly Journal of the Royal Meteorological Society, 131(609), 2081--2107, 2005.
- Zhou17
- Qi Zhou , John R. Taylor , C. P. Caulfield (2017), Self-similar mixing in stratified plane { Couette } flow for varying { Prandtl } number, Journal of Fluid Mechanics, 820, 86--120, 2017.
- sagaut06
- P. Sagaut , C. Meneveau (2006), { Large Eddy Simulation for Incompressible Flows: An Introduction }, Springer, 2006.
- vanRoekel18
- Luke Van Roekel , Alistair J. Adcroft , Gokhan Danabasoglu , Stephen M. Griffies , Brian Kauffman , William Large , Michael Levy , Brandon G. Reichl , Todd Ringler , Martin Schmidt (2018), The { KPP } { Boundary } { Layer } { Scheme } for the { Ocean } : { Revisiting } { Its } { Formulation } and { Benchmarking } { One } ‐ { Dimensional } { Simulations } { Relative } to { LES }, Journal of Advances in Modeling Earth Systems, 10(11), 2647--2685, 2018.