Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2006, Volume 195, Issue 44-47, pp. 6011 - 6045

A series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper. These...

Navierâ€“Stokes equations | Finite elements | Spectral approximations | Incompressibility | Projection methods | Fractional step methods | Navier-Stokes equations | ACCURATE | projection methods | 2ND-ORDER | APPROXIMATION | GALERKIN METHOD | TIME | SOLVERS | fractional step methods | SCHEME | incompressibility | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | spectral approximations | IMPLEMENTATIONS | CONVERGENCE | finite elements | Finite element method | Analysis | Methods

Navierâ€“Stokes equations | Finite elements | Spectral approximations | Incompressibility | Projection methods | Fractional step methods | Navier-Stokes equations | ACCURATE | projection methods | 2ND-ORDER | APPROXIMATION | GALERKIN METHOD | TIME | SOLVERS | fractional step methods | SCHEME | incompressibility | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | spectral approximations | IMPLEMENTATIONS | CONVERGENCE | finite elements | Finite element method | Analysis | Methods

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 05/2015, Volume 771, pp. 79 - 114

In this paper we investigate the Tayler instability in an incompressible, viscous and resistive liquid metal column and in a model of a liquid metal battery...

Papers | multiphase and particle-laden flows | multiphase flow | MHD and electrohydrodynamics | MECHANICS | FLUID | PHYSICS, FLUIDS & PLASMAS | STABILITY | GALLIUM EXPERIMENT | ENERGY-STORAGE | TOROIDAL MAGNETIC-FIELDS | ANTIMONY | CELL | Fluid mechanics | Flow velocity | Numerical analysis | Batteries

Papers | multiphase and particle-laden flows | multiphase flow | MHD and electrohydrodynamics | MECHANICS | FLUID | PHYSICS, FLUIDS & PLASMAS | STABILITY | GALLIUM EXPERIMENT | ENERGY-STORAGE | TOROIDAL MAGNETIC-FIELDS | ANTIMONY | CELL | Fluid mechanics | Flow velocity | Numerical analysis | Batteries

Journal Article

EPL, ISSN 0295-5075, 06/2016, Volume 114, Issue 6, pp. 65002 - 65002

For the first time, a direct numerical simulation of the incompressible, fully nonlinear, magnetohydrodynamic (MHD) equations for the Von Karman Sodium (VKS)...

EQUATIONS | INDUCTION | PHYSICS, MULTIDISCIPLINARY | DOMAINS | FLOW | Magnetohydrodynamics | Rotating generators | Sodium | Computational fluid dynamics | Thresholds | Impellers | Reynolds number | Fluid flow | Mechanics | Mechanics of the fluids | Physics

EQUATIONS | INDUCTION | PHYSICS, MULTIDISCIPLINARY | DOMAINS | FLOW | Magnetohydrodynamics | Rotating generators | Sodium | Computational fluid dynamics | Thresholds | Impellers | Reynolds number | Fluid flow | Mechanics | Mechanics of the fluids | Physics

Journal Article

4.
Full Text
Mean-field model of the von KÃ¡rmÃ¡n sodium dynamo experiment using soft iron impellers

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 01/2015, Volume 91, Issue 1, p. 013008

It has been observed that dynamo action occurs in the von-Karman-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The...

PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | FLOW | Mechanics | Mechanics of the fluids | Physics

PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | FLOW | Mechanics | Mechanics of the fluids | Physics

Journal Article

New Journal of Physics, ISSN 1367-2630, 05/2012, Volume 14, Issue 5, pp. 53005 - 053005_16

Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-Karman-sodium dynamo experiment. The...

KINEMATIC DYNAMOS | VOLUME METHOD | LABORATORY MODEL | PHYSICS, MULTIDISCIPLINARY | GEOMAGNETIC DYNAMO | FIELD | FLOWS | SIMULATION | DOMAINS | Physics - Fluid Dynamics | Mechanics | Mechanics of the fluids | Physics

KINEMATIC DYNAMOS | VOLUME METHOD | LABORATORY MODEL | PHYSICS, MULTIDISCIPLINARY | GEOMAGNETIC DYNAMO | FIELD | FLOWS | SIMULATION | DOMAINS | Physics - Fluid Dynamics | Mechanics | Mechanics of the fluids | Physics

Journal Article

Geophysical Journal International, ISSN 0956-540X, 2014, Volume 197, Issue 1, pp. 119 - 134

Convection in planetary cores can generate fluid flow and magnetic fields, and a number of sophisticated codes exist to simulate the dynamic behaviour of such...

Planetary interiors | Dynamo:theories and simulations | Non-linear differential equations | Numerical solutions | GEOCHEMISTRY & GEOPHYSICS | CONVECTION-DRIVEN DYNAMOS | Dynamo: theories and simulations | EQUATIONS | SIMULATION | CONDUCTING INNER-CORE | Mechanics | Mechanics of the fluids | Physics

Planetary interiors | Dynamo:theories and simulations | Non-linear differential equations | Numerical solutions | GEOCHEMISTRY & GEOPHYSICS | CONVECTION-DRIVEN DYNAMOS | Dynamo: theories and simulations | EQUATIONS | SIMULATION | CONDUCTING INNER-CORE | Mechanics | Mechanics of the fluids | Physics

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2006, Volume 195, Issue 44, pp. 5857 - 5876

A subgrid stabilization technique is developed for solving the two-dimensional incompressible Navierâ€“Stokes equations at high Reynolds numbers. The time...

Navierâ€“Stokes equations | Finite elements | Subgrid stabilization | Incompressibility | 2D flows at high Reynolds numbers | Projection methods | Navier-Stokes equations | projection methods | APPROXIMATIONS | incompressibility | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | COMPUTATIONAL FLUID-DYNAMICS | CONVERGENCE | FINITE-ELEMENT FORMULATION | subgrid stabilization | finite elements | Statistics | Methods | Algorithms

Navierâ€“Stokes equations | Finite elements | Subgrid stabilization | Incompressibility | 2D flows at high Reynolds numbers | Projection methods | Navier-Stokes equations | projection methods | APPROXIMATIONS | incompressibility | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | COMPUTATIONAL FLUID-DYNAMICS | CONVERGENCE | FINITE-ELEMENT FORMULATION | subgrid stabilization | finite elements | Statistics | Methods | Algorithms

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 02/2003, Volume 41, Issue 1, pp. 112 - 134

...SIAM J. NUMER. ANAL. c Vol. 41, No. 1, pp. 112134 VELOCITY-CORRECTION PROJECTION METHODS FOR INCOMPRESSIBLE FLOWS J. L. GUERMOND AND JIE SHEN Abstract...

Finite elements | Spectral approximations | Fractional-step methods | Incompressibility | Projection methods | Navier-Stokes equations | MATHEMATICS, APPLIED | incompressibility | projection methods | 2ND-ORDER | spectral approximations | fractional-step methods | CAVITY | finite elements | SCHEMES

Finite elements | Spectral approximations | Fractional-step methods | Incompressibility | Projection methods | Navier-Stokes equations | MATHEMATICS, APPLIED | incompressibility | projection methods | 2ND-ORDER | spectral approximations | fractional-step methods | CAVITY | finite elements | SCHEMES

Journal Article

Physical Review Letters, ISSN 0031-9007, 09/2008, Volume 101, Issue 10, p. 104501

In the von Karman Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying...

PHYSICS, MULTIDISCIPLINARY | FLOW | Physics - Fluid Dynamics | Fluid Dynamics | Physics | MAGNETIC FIELDS | AXIAL SYMMETRY | SODIUM | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | TURBULENCE | MAGNETIC REYNOLDS NUMBER | GEOSCIENCES | SIMULATION | BOUNDARY CONDITIONS

PHYSICS, MULTIDISCIPLINARY | FLOW | Physics - Fluid Dynamics | Fluid Dynamics | Physics | MAGNETIC FIELDS | AXIAL SYMMETRY | SODIUM | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | TURBULENCE | MAGNETIC REYNOLDS NUMBER | GEOSCIENCES | SIMULATION | BOUNDARY CONDITIONS

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2011, Volume 200, Issue 23, pp. 2083 - 2093

We introduce in this paper a new direction splitting algorithm for solving the incompressible Navierâ€“Stokes equations. The main originality of the method...

Pressure Poisson equation | 76D30 | 65N35 | Direction splitting | ADI | Incompressible flows | Navierâ€“Stokes | 35J05 | 76M20 | Time splitting | 65F05 | Navier-Stokes | PROJECTION METHODS | FLOW | DRIVEN CAVITY | FICTITIOUS DOMAIN | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Operators | Splitting | Algorithms | Mathematical analysis | Projection | Mathematical models | Convergence | Navier-Stokes equations

Pressure Poisson equation | 76D30 | 65N35 | Direction splitting | ADI | Incompressible flows | Navierâ€“Stokes | 35J05 | 76M20 | Time splitting | 65F05 | Navier-Stokes | PROJECTION METHODS | FLOW | DRIVEN CAVITY | FICTITIOUS DOMAIN | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Operators | Splitting | Algorithms | Mathematical analysis | Projection | Mathematical models | Convergence | Navier-Stokes equations

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2005, Volume 43, Issue 1, pp. 239 - 258

... CONDITIONS J. L. GUERMOND, P. MINEV, AND J. SHEN Abstract. The incompressible Stokes equations with prescribed normal stress (open) boundary conditions on part...

Open boundary conditions | Finite elements | Spectral approximations | Pressure-correction methods | Incompressibility | Navier-Stokes and Stokes equations | MATHEMATICS, APPLIED | CONSISTENT MASS MATRIX | 2ND-ORDER | APPROXIMATION | pressure-correction methods | FRACTIONAL STEP METHOD | IMPLEMENTATION | SEMIIMPLICIT PROJECTION METHODS | incompressibility | open boundary conditions | spectral approximations | CONVERGENCE | VISCOUS INCOMPRESSIBLE-FLOW | finite elements | FINITE-ELEMENT METHOD

Open boundary conditions | Finite elements | Spectral approximations | Pressure-correction methods | Incompressibility | Navier-Stokes and Stokes equations | MATHEMATICS, APPLIED | CONSISTENT MASS MATRIX | 2ND-ORDER | APPROXIMATION | pressure-correction methods | FRACTIONAL STEP METHOD | IMPLEMENTATION | SEMIIMPLICIT PROJECTION METHODS | incompressibility | open boundary conditions | spectral approximations | CONVERGENCE | VISCOUS INCOMPRESSIBLE-FLOW | finite elements | FINITE-ELEMENT METHOD

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 11/2018, Volume 854, pp. 164 - 195

We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flows in the von KÃ¡rmÃ¡n sodium (VKS) set-up. The counter-rotating impellers...

JFM Papers | dynamo theory | MHD and electrohydrodynamics | UNSTEADY FLOWS | MECHANICS | KINEMATIC DYNAMOS | REGULARITY | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | TURBULENCE | INDUCTION | DOMAINS | GEOMETRY | Magnetohydrodynamics | Dipoles | Fluid flow | Iron | Experiments | Large eddy simulation | Impellers | Kinematics | Mathematical models | Liquid sodium | Computer simulation | Computational fluid dynamics | Reynolds number | Hydrodynamics | Permeability | Grants | Rotation | Velocity | Geometry | Numerical analysis | Sodium | Simulation | Laminar flow | Magnetic permeability | Vortices | Magnetic fields | Mechanics | Mechanics of the fluids | Mathematics | Numerical Analysis | Physics

JFM Papers | dynamo theory | MHD and electrohydrodynamics | UNSTEADY FLOWS | MECHANICS | KINEMATIC DYNAMOS | REGULARITY | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | TURBULENCE | INDUCTION | DOMAINS | GEOMETRY | Magnetohydrodynamics | Dipoles | Fluid flow | Iron | Experiments | Large eddy simulation | Impellers | Kinematics | Mathematical models | Liquid sodium | Computer simulation | Computational fluid dynamics | Reynolds number | Hydrodynamics | Permeability | Grants | Rotation | Velocity | Geometry | Numerical analysis | Sodium | Simulation | Laminar flow | Magnetic permeability | Vortices | Magnetic fields | Mechanics | Mechanics of the fluids | Mathematics | Numerical Analysis | Physics

Journal Article

Journal of computational physics, ISSN 0021-9991, 2009, Volume 228, Issue 8, pp. 2834 - 2846

A new fractional time-stepping technique for solving incompressible flows with variable density is proposed. The main feature of this method is that, as...

Projection method | Fractional time-stepping | Navierâ€“Stokes | Variable density flows | Navier-Stokes | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | APPROXIMATION | FINITE-ELEMENT | CONVERGENCE | PHYSICS, MATHEMATICAL | PROJECTION METHODS | Methods | Algorithms | Incompressible flow | Splitting | Fluid flow | Poisson equation | Mathematical models | Computational efficiency | Density

Projection method | Fractional time-stepping | Navierâ€“Stokes | Variable density flows | Navier-Stokes | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | APPROXIMATION | FINITE-ELEMENT | CONVERGENCE | PHYSICS, MATHEMATICAL | PROJECTION METHODS | Methods | Algorithms | Incompressible flow | Splitting | Fluid flow | Poisson equation | Mathematical models | Computational efficiency | Density

Journal Article

Journal of Physics: Conference Series, ISSN 1742-6588, 2011, Volume 318, Issue 7, pp. 1 - 3

...) 072034 doi:10.1088/1742-6596/318/7/072034 Nonlinear dynamo action in a cylindrical container driven by precession C. Nore 1 , J. L eorat 2 , J.-L. Guermond 3;4 & F...

Magnetohydrodynamics | Rotating generators | Precession | Sodium | Computational fluid dynamics | Containers | Nonlinearity | Thermohydraulics | Three dimensional

Magnetohydrodynamics | Rotating generators | Precession | Sodium | Computational fluid dynamics | Containers | Nonlinearity | Thermohydraulics | Three dimensional

Conference Proceeding

Journal of fluid mechanics, ISSN 1469-7645, 2019, Volume 878, pp. 598 - 646

We propose a new theoretical model for metal pad roll instability in idealized cylindrical reduction cells. In addition to the usual destabilizing effects, we...

ALUMINUM ELECTROLYSIS CELLS | MELT FLOWS | PHYSICS, FLUIDS & PLASMAS | STABILITY | SURFACE-WAVES | MHD | ELECTRODES | SIMULATION | SHALLOW-WATER MODEL | BATTERIES | MECHANICS | multiphase flow | INTERFACE INSTABILITY | Perturbation theory | Damping | Magnetohydrodynamics | Computational fluid dynamics | Metals | Gravitational waves | Fluid flow | Benchmarks | Liquid metals | Product design | Batteries | Cells | Viscous damping | Interfaces | Reduction | Energy dissipation | Solvers | Instability | Control stability | Gravity waves | Cylinders

ALUMINUM ELECTROLYSIS CELLS | MELT FLOWS | PHYSICS, FLUIDS & PLASMAS | STABILITY | SURFACE-WAVES | MHD | ELECTRODES | SIMULATION | SHALLOW-WATER MODEL | BATTERIES | MECHANICS | multiphase flow | INTERFACE INSTABILITY | Perturbation theory | Damping | Magnetohydrodynamics | Computational fluid dynamics | Metals | Gravitational waves | Fluid flow | Benchmarks | Liquid metals | Product design | Batteries | Cells | Viscous damping | Interfaces | Reduction | Energy dissipation | Solvers | Instability | Control stability | Gravity waves | Cylinders

Journal Article

Geophysical Journal International, ISSN 0956-540X, 2014, Volume 196, Issue 2, pp. 712 - 723

It is frequently considered that many planetary magnetic fields originate as a result of convection within planetary cores. Buoyancy forces responsible for...

Non-linear differential equations | Dynamo | theories and simulations | Electromagnetic theory | CORE | GEOCHEMISTRY & GEOPHYSICS | CONVECTION-DRIVEN DYNAMOS | INCOMPRESSIBLE FLOWS | FLUID SHELLS | Dynamo: theories and simulations | EQUATIONS | SIMULATION | MANTLE | Mechanics | Mechanics of the fluids | Physics

Non-linear differential equations | Dynamo | theories and simulations | Electromagnetic theory | CORE | GEOCHEMISTRY & GEOPHYSICS | CONVECTION-DRIVEN DYNAMOS | INCOMPRESSIBLE FLOWS | FLUID SHELLS | Dynamo: theories and simulations | EQUATIONS | SIMULATION | MANTLE | Mechanics | Mechanics of the fluids | Physics

Journal Article

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, ISSN 0271-2091, 05/1998, Volume 26, Issue 9, pp. 1039 - 1053

This work investigates the proper choices of spatial approximations for velocity and pressure in fractional-step projection methods. Numerical results obtained...

incompressible Navier-Stokes equations | INCOMPRESSIBLE-FLOW | PHYSICS, FLUIDS & PLASMAS | pressure Poisson equation | projection method | fractional-step method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | stabilization methods | IMPLEMENTATIONS | finite elements | FINITE-ELEMENT METHOD

incompressible Navier-Stokes equations | INCOMPRESSIBLE-FLOW | PHYSICS, FLUIDS & PLASMAS | pressure Poisson equation | projection method | fractional-step method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | stabilization methods | IMPLEMENTATIONS | finite elements | FINITE-ELEMENT METHOD

Journal Article

SIAM journal on numerical analysis, ISSN 0036-1429, 1/2006, Volume 44, Issue 2, pp. 753 - 778

...SIAM J. NUMER. ANAL. c Vol. 44, No. 2, pp. 753778 DISCONTINUOUS GALERKIN METHODS FOR FRIEDRICHS SYSTEMS. I. GENERAL THEORY A. ERN AND J.-L. GUERMOND Abstract...

Finite element method | Mathematical discontinuity | Approximation | Adjoints | Vector fields | Boundary conditions | Maxwell equations | Galerkin methods | Estimation methods | Discontinuous Galerkin method | Finite elements | Friedrichs' systems | Partial differential equations | MATHEMATICS, APPLIED | discontinuous Galerkin method | INTERIOR PENALTY | DIFFERENTIAL-EQUATIONS | DIFFUSION-PROBLEMS | partial differential equations | FINITE-ELEMENT-METHOD | finite elements

Finite element method | Mathematical discontinuity | Approximation | Adjoints | Vector fields | Boundary conditions | Maxwell equations | Galerkin methods | Estimation methods | Discontinuous Galerkin method | Finite elements | Friedrichs' systems | Partial differential equations | MATHEMATICS, APPLIED | discontinuous Galerkin method | INTERIOR PENALTY | DIFFERENTIAL-EQUATIONS | DIFFUSION-PROBLEMS | partial differential equations | FINITE-ELEMENT-METHOD | finite elements

Journal Article

Numerische Mathematik, ISSN 0029-599X, 08/1998, Volume 80, Issue 2, pp. 207 - 238

This paper provides an analysis of a fractional-step projection method to compute incompressible viscous flows by means of finite element approximations. The...

Mathematics Subject Classification :35Q30, 65M12, 65M60 | MATHEMATICS, APPLIED | TIME | SPATIAL DISCRETIZATION | REGULARITY | IMPLEMENTATIONS

Mathematics Subject Classification :35Q30, 65M12, 65M60 | MATHEMATICS, APPLIED | TIME | SPATIAL DISCRETIZATION | REGULARITY | IMPLEMENTATIONS

Journal Article

20.