, Projection methods for the Navier-Stokes equations, p.65
68 2.5.3 On the resolution by the Finite Elements method, p.69 ,
Finite Elements methods for the free surface Navier-Stokes equations with pressure decomposition, p.69 ,
,
155 5.3.1 Characterization of the regimes, p.161 ,
, Treatment of the dispersion relation
,
,
Residual distribution schemes: current status and future trends, Computers & Fluids, vol.35, issue.7, pp.641-669, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00403695
, J. J. Sobolev spaces, vol.140, 2003.
Tides and Waves: Extracted from the Encyclopaedia Metropolitana, p.1845 ,
Vectors, tensors and the basic equations of fluid mechanics. Courier Corporation, 2012. ,
A multilayer saint-venant model: derivation and numerical validation, Discrete & Continuous Dynamical Systems-B, vol.5, pp.189-214, 2005. ,
Finite-volume solvers for a multilayer saintvenant system, International Journal of Applied Mathematics and Computer Science, vol.17, pp.311-320, 2007. ,
Parametric study of the accuracy of an approximate solution for the mild-slope equation, 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC, pp.79-85, 2017. ,
CFD simulation of free-surface flow over triangular labyrinth side weir, Advances in Engineering Software, vol.45, pp.159-166, 2012. ,
A second-order projection method for the incompressible Navier-Stokes equations, Journal of Computational Physics, vol.85, pp.257-283, 1989. ,
Computation of combined refraction-diffraction, Coastal Engineering, pp.471-490, 1973. ,
Mathematical models for simple harmonic linear water waves: wave diffraction and refraction, 1976. ,
A description of a three-dimensional coastal ocean circulation model, Three-dimensional coastal ocean models, vol.4, pp.1-16, 1987. ,
Stability and geometric conservation laws for ALE formulations, Computer methods in applied mechanics and engineering, vol.193, pp.4717-4739, 2004. ,
Modified pressure-correction projection methods: Open boundary and variable time stepping, Numerical Mathematics and Advanced Applications-ENUMATH 2013, pp.623-631, 2015. ,
Time-discrete higher-order ALE formulations: stability, SIAM Journal on Numerical Analysis, vol.51, pp.577-604, 2013. ,
Gravity waves on water with non-uniform depth and current, 1981. ,
A note on the accuracy of the mild-slope equation, Coastal Engineering, vol.7, issue.3, pp.191-203, 1983. ,
Stabilized finite element methods for the generalized Oseen problem, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.853-866, 2007. ,
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers. Publications mathématiques et informatique de Rennes, vol.4, pp.1-26, 1974. ,
Mixed and hybrid finite element methods, vol.15, 2012. ,
SUPG formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comp Methods Appl Mech Eng, vol.32, pp.199-259, 1982. ,
A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty, SIAM journal on numerical analysis, vol.43, pp.2012-2033, 2005. ,
Consistent supg-method for transient transport problems: Stability and convergence, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.1114-1123, 2010. ,
A monotonicity preserving, nonlinear, finite element upwind method for the transport equation, Applied Mathematics Letters, vol.49, pp.141-146, 2015. ,
Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems, SIAM Journal on Numerical Analysis, vol.48, pp.2019-2042, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00380659
Edge stabilization for galerkin approximations of convection-diffusion-reaction problems, Computer Methods in Applied Mechanics and Engineering, vol.193, pp.1437-1453, 2004. ,
A semi-implicit finite difference method for non-hydrostatic, freesurface flows, International Journal for Numerical Methods in Fluids, vol.30, pp.425-440, 1999. ,
A semi-implicit finite difference method for the free-surface Navier-Stokes equations, Int. J. Numer. Methods Fluids, vol.74, pp.605-622, 2014. ,
,
accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow, Computers & Mathematics with Applications, vol.27, pp.99-112, 1994. ,
Semi-implicit finite difference methods for three-dimensional shallow water flow, International Journal for numerical methods in fluids, vol.15, pp.629-648, 1992. ,
Simulation of three-dimensional, nonhydrostatic free-surface flows for estuaries and coastal seas, Estuarine and coastal modeling, pp.1-12, 1995. ,
Numerical simulation of 3D quasi-hydrostatic, free-surface flows, Journal of Hydraulic Engineering, vol.124, pp.678-686, 1998. ,
An unstructured grid, three-dimensional model based on the shallow water equations, International journal for numerical methods in fluids, vol.32, pp.331-348, 2000. ,
Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems, Mathematical and computer modelling, vol.36, pp.1131-1149, 2002. ,
The lumped mass finite element method for a parabolic problem, The ANZIAM Journal, vol.26, pp.329-354, 1985. ,
Effects of bottom friction and boundary absorption on water wave scattering, Applied Ocean Research, vol.8, pp.99-104, 1986. ,
Oscillations and wave forces in a man-made harbor in the open sea, Symposium on Naval Hydrodynamics, 10th, Proceedings, Pap and Discuss, 1974. ,
Numerical solution of the Navier-Stokes equations, Mathematics of computation, vol.22, pp.745-762, 1968. ,
Fast accurate computation of the fully nonlinear solitary surface gravity waves, Computers & fluids, vol.84, pp.35-38, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00759812
, Discontinuous Galerkin methods: theory, computation and applications, vol.11, 2012.
Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods, Computer methods in applied mechanics and engineering, vol.190, pp.1579-1599, 2000. ,
Stabilized finite element approximation of transient incompressible flows using orthogonal subscales, Computer Methods in Applied Mechanics and Engineering, vol.191, pp.4295-4321, 2002. ,
Water wave mechanics for engineers and scientists, vol.2, 1991. ,
Hydrostatic model for three-dimensional free surface flows and numerical schemes, 2006. ,
URL : https://hal.archives-ouvertes.fr/tel-00180003
Sigma transformation and ALE formulation for three-dimensional free surface flows, International Journal for Numerical Methods in Fluids, vol.59, pp.357-386, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00541170
Moving meshes with freefem++, Journal of Numerical Mathematics, vol.20, pp.195-214, 2012. ,
Water wave propagation over uneven bottoms, vol.13, 1997. ,
Finite element solution of the unsteady Navier-Stokes equations by a fractional step method, Computer Methods in Applied Mechanics and Engineering, vol.30, pp.53-73, 1982. ,
Implicit free surface method for the Bryan-Cox-Semtner ocean model, Journal of Geophysical Research: Oceans, vol.99, pp.7991-8014, 1994. ,
The propagation of gravity waves from deep to shallow water, Gravity waves, p.165, 1952. ,
Telemac Modelling System. Theoretical Note and User Manual. Artemis Software Wave Agitation, 2010. ,
The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow, International Journal for Numerical Methods in Fluids, vol.2, pp.225-238, 1982. ,
Theory and practice of finite elements, vol.159, 2013. ,
On calculating the lengths of water waves, Coastal Engineering, vol.14, pp.499-513, 1990. ,
Differentiation under the integral sign, The American Mathematical Monthly, vol.80, pp.615-627, 1973. ,
A finite element method for 3D hydrostatic water flows. Computing and Visualization in Science, vol.2, pp.85-93, 1999. ,
A stability analysis for the Arbitrary Lagrangian Eulerian formulation with finite elements, East-West Journal of Numerical Mathematics, vol.7, pp.105-132, 1999. ,
Stability analysis of second-order time accurate schemes for ALE-FEM, Computer methods in applied mechanics and engineering, vol.193, pp.4097-4116, 2004. ,
, Finite-Difference Methods for Partial Differential Equations, 1960.
An unstructured-grid, finitevolume, nonhydrostatic, parallel coastal ocean simulator, Ocean Modelling, vol.14, pp.139-173, 2006. ,
ALE-SUPG finite element method for convection-diffusion problems in time-dependent domains: Conservative form, Applied Mathematics and Computation, vol.303, pp.128-145, 2017. ,
Estimate of truncation error in transformed coordinate primite equation atmospheric models, J. Atmso. Sci, vol.30, pp.223-233, 1973. ,
On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via finite element method that also introduces a nearly consistent mass matrix. part i and part ii, Int. J. Numer. Methods Fluids, vol.11, pp.587-620, 1990. ,
Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra, Numerische Mathematik, vol.131, pp.771-822, 2015. ,
A multistep technique with implicit difference schemes for calculating two-or three-dimensional cavity flows, Journal of Computational Physics, vol.30, pp.76-95, 1979. ,
On Cauchy's equations of motion, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), vol.15, pp.290-292, 1964. ,
An overview of projection methods for incompressible flows, Computer methods in applied mechanics and engineering, vol.195, pp.6011-6045, 2006. ,
Error analysis of pressure-correction schemes for the time-dependent stokes equations with open boundary conditions, SIAM Journal on Numerical Analysis, vol.43, pp.239-258, 2005. ,
On the error estimates for the rotational pressurecorrection projection methods, Mathematics of Computation, vol.73, pp.1719-1737, 2004. ,
Stabilization of galerkin approximations of transport equations by subgrid modeling, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, pp.1293-1316, 1999. ,
Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, pp.169-189, 1999. ,
Subgrid stabilization of galerkin approximations of linear monotone operators, IMA Journal of Numerical Analysis, vol.21, pp.165-197, 2001. ,
A correction technique for the dispersive effects of mass lumping for transport problems, Computer Methods in Applied Mechanics and Engineering, vol.253, pp.186-198, 2013. ,
URL : https://hal.archives-ouvertes.fr/ujm-00860583
On stability and convergence of projection methods based on pressure poisson equation, International Journal for Numerical Methods in Fluids, vol.26, pp.1039-1053, 1998. ,
, , 2005.
Hydrodynamics of free surface flows, modelling with finite element method, 2007. ,
An arbitrary lagrangian-eulerian computing method for all flow speeds, J. Comput. Phys, vol.14, issue.3, pp.227-253, 1974. ,
Numerical techniques in cwr-elcom (code release v. 1). CWR Manuscript WP, p.1422, 2000. ,
Viscous flow with large free surface motion, Computer Methods in Applied Mechanics and Engineering, vol.69, pp.277-324, 1988. ,
A new finite element formulation for computational fluid dynamics: V. circumventing the babu?ka-brezzi condition: A stable petrov-galerkin formulation of the stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering, vol.59, pp.85-99, 1986. ,
A new finite element formulation for computational fluid dynamics: Viii. the galerkin/least-squares method for advective-diffusive equations, Computer methods in applied mechanics and engineering, vol.73, pp.173-189, 1989. ,
Direct solution of wave dispersion equation, Journal of the Waterway, Port, Coastal and Ocean Division, vol.105, pp.457-459, 1979. ,
Pressure gradient force and advection scheme used for forecasting with steep and small scale topography, Contrib. Atmos. Phys, vol.50, pp.186-199, 1977. ,
Openfoam: open source cfd in research and industry, International Journal of Naval Architecture and Ocean Engineering, vol.1, pp.89-94, 2009. ,
Finite element methods for incompressible flow problems, 2016. ,
Error analysis of the SUPG finite element discretization of evolutionary convection-diffusion-reaction equations, SIAM Journal on Numerical Analysis, vol.49, pp.1149-1176, 2011. ,
Algorithm for nonhydrostatic dynamics in the regional oceanic modeling system, Ocean Modelling, vol.18, pp.143-174, 2007. ,
A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations, J. Comput. Phys, vol.70, pp.439-462, 1987. ,
A nonhydrostatic version of fvcom: 1. validation experiments, Journal of Geophysical Research: Oceans, vol.115, p.11, 2010. ,
,
The water waves problem: mathematical analysis and asymptotics, vol.188, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01101991
Stability analysis of pressure correction schemes for the Navier-Stokes equations with traction boundary conditions, Computer Methods in Applied Mechanics and Engineering, vol.309, pp.307-324, 2016. ,
A new incompressible SPH model: towards industrial applications, 2014. ,
URL : https://hal.archives-ouvertes.fr/tel-01128612
Geometric conservation laws for flow problems with moving boundaries and deformable meshes and their impact on aerolastic computations, Comput. Methods Appl. Mech. Eng, vol.134, pp.71-90, 1996. ,
Development and validation of a three-dimensional morphological model, Coastal engineering, vol.51, pp.883-915, 2004. ,
Efficient elliptic solvers for the mild-slope equation using the multigrid technique, Coastal Engineering, vol.16, pp.245-266, 1992. ,
Leakage and response of waves trapped by round islands, The Physics of Fluids, vol.19, pp.1075-1088, 1976. ,
ADCIRC: An Advanced Three-Dimensional Circulation Model forShelves, Coasts, and Estuaries. Report 1. Theory and Methodology of ADCIRC-2DDI and ADCIRC-3DL, DL. Tech. rep, 1992. ,
A nonhydrostatic mesoscale ocean model. part ii: Numerical implementation, Journal of Physical Oceanography, vol.26, pp.1881-1900, 1996. ,
A finite-volume, incompressible Navier-Stokes model for studies of the ocean on parallel computers, Journal of Geophysical Research: Oceans, vol.102, pp.5753-5766, 1997. ,
Characteristics ale method for the unsteady 3d Navier-Stokes equations with a free surface, International Journal of Computational Fluid Dynamics, vol.6, pp.175-188, 1996. ,
, Theory and Applications of Ocean Surface Waves: Part, vol.1, 1989.
Finite element approximation of quasi-3d shallow water equations, Comput. Methods Appl. Mech. Engrg, vol.174, pp.355-369, 1999. ,
An existence and uniqueness result for the 3D Shallow Water Equations. Internal Report n. 421/P. Dipartimiento di Matematica Francesco Brioschi, 2000. ,
Smoothed particle hydrodynamics, Reports on progress in physics, vol.68, p.1703, 2005. ,
An eulerian finite element method for timedependent free surface problems in hydrodynamics, International Journal for Numerical Methods in Fluids, vol.22, pp.175-194, 1996. ,
Explicit formulae for practical wave calculations, Coastal Engineering, vol.6, pp.389-398, 1982. ,
Theoritical and practical aspects of some boundary value problems in fluid dynamics, SIAM J. Applied Mathematics, vol.35, pp.419-446, 1978. ,
Compact cell vertex convection schemes on unstructured meshes, Problèmes non linéaires appliqués. Ecoles CEA-EDF-INRIA, pp.91-139, 2000. ,
Solution of the mild-slope wave problem by iteration, Applied Ocean Research, vol.13, pp.187-199, 1991. ,
Approximation de la solution des équations d'un modèle de turbulence par une methode de lagrange-galerkin, Rev. Mat. Apl, vol.15, pp.63-124, 1994. ,
Nouveaux schémas de convection pour les écoulements à surface libre, 2016. ,
A coordinate system having some special advantages for numerical forecasting, J Meteorol, vol.14, pp.184-185, 1957. ,
On the transport-diffusion algorithm and its applications to the Navier-Stokes equations, Numerische Mathematik, vol.38, pp.309-332, 1982. ,
Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations, 1997. ,
, Numerical Approximation of Partial Differential E Springer Ser. Comput. Math, vol.23, 1994.
On Chorin's projection method for the incompressible navierstokes equations, The Navier-Stokes equations II-theory and numerical methods, pp.167-183, 1992. ,
Hyperbolic partial differential equations and geometric optics, vol.133, 2012. ,
Papers on Mechanical and Physical Subjects: The sub-mechanics of the universe, vol.3, 1903. ,
Robust numerical methods for singularly perturbed differential equations: convection-diffusion-reaction and flow problems, vol.24, 2008. ,
Flow-3d Theory manual, 2002. ,
The regional ocean model system (ROMS): A split-explicit, free-surface, topography-following coordinate ocean model, Ocean Modelling, vol.9, pp.347-404, 2005. ,
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes, Mathematics of Computation of the American Mathematical Society, vol.65, pp.1039-1065, 1996. ,
On the theory of oscillatory waves, Transactions of the Cambridge Philosophical Society, 1880. ,
Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires ii, Arch. Ration. Mech. Anal, vol.33, pp.377-385, 1969. ,
Navier-Stokes Equations: Theory and Numerical Analysis, 1984. ,
Stabilized finite element formulations for incompressible flow computations, Advances in applied mechanics, vol.28, pp.1-44, 1991. ,
An approximate projection scheme for incompressible flow using spectral elements, International journal for numerical methods in fluids, vol.22, pp.673-688, 1996. ,
A finite element model for wave refraction and diffraction, Applied Ocean Research, vol.5, pp.30-37, 1983. ,
Inversion of a tridiagonal jacobi matrix, Linear Algebra and its Applications, vol.212, pp.413-414, 1994. ,
A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Stat. Comput, vol.7, issue.3, pp.870-891, 1986. ,
Direct solution of wave dispersion equation, Journal of the Waterway Ports Coastal and Ocean Engineering Division ASCE, vol.106, pp.501-502, 1980. ,
Finite Element approximations on steady Navier-Stokes equations with mixed boundary conditions, Mod Math. Anal. Numer, vol.19, pp.461-475, 1985. ,
Fluid mechanics and the SPH method: theory and applications, 2012. ,
Stability and consistency of nonhydrostatic free-surface models using the semi-implicit ?-method, International Journal for Numerical Methods in Fluids, vol.72, pp.550-582, 2013. ,
Mike 21: a modelling system for estuaries, coastal waters and seas, Environmental Software, vol.7, pp.229-240, 1992. ,
Projection method I: Convergence and numerical boundary layers, SIAM J. Numer. Anal, vol.32, pp.1017-1057, 1995. ,
Linear and nonlinear waves, vol.42, p.182, 2011. ,
Stability of periodic waves of finite amplitude on the surface of a deep fluid, Journal of Applied Mechanics and Technical Physics, vol.9, pp.190-194, 1968. ,
, The Schur complement and its applications, vol.4, 2006.
Selfe: a semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation, Ocean modelling, vol.21, pp.71-96, 2008. ,