Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 07/2014, Volume 140, Issue 682, pp. 1505 - 1520

Following previous work on an inherently mass‐conserving semi‐implicit (SI) semi‐Lagrangian (SL) discretization of the two‐dimensional (2D) shallow‐water...

spatial discretization | C‐grid | spheroidal coordinates | temporal discretization | Charney–Phillips | SLICE | Spatial discretization | Charney-Phillips | Spheroidal coordinates | Temporal discretization | C-grid | SPHERE | NORMAL-MODES | FORMULATION | VERTICAL COORDINATE | SHALLOW-WATER EQUATIONS | SCHEME | INTEGRATION | VECTOR EQUATIONS | METEOROLOGY & ATMOSPHERIC SCIENCES | EULER EQUATIONS | Atmosphere | Hydrostatics | Discretization | Mathematical analysis | Preserves | Mathematical models | Two dimensional | Standards | Three dimensional

spatial discretization | C‐grid | spheroidal coordinates | temporal discretization | Charney–Phillips | SLICE | Spatial discretization | Charney-Phillips | Spheroidal coordinates | Temporal discretization | C-grid | SPHERE | NORMAL-MODES | FORMULATION | VERTICAL COORDINATE | SHALLOW-WATER EQUATIONS | SCHEME | INTEGRATION | VECTOR EQUATIONS | METEOROLOGY & ATMOSPHERIC SCIENCES | EULER EQUATIONS | Atmosphere | Hydrostatics | Discretization | Mathematical analysis | Preserves | Mathematical models | Two dimensional | Standards | Three dimensional

Journal Article

Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 01/2013, Volume 139, Issue 670, pp. 152 - 175

This study describes a new global non‐hydrostatic dynamical core (ICON‐IAP: Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics) on a...

global atmospheric modelling | Lorenz energy cycle | hexagonal C‐grid | Global atmospheric modelling | Hexagonal C-grid | SENSITIVITY | MODEL | FORMULATION | VORTICITY | GENERAL-METHOD | hexagonal C-grid | SCHEME | POTENTIAL ENSTROPHY | DIFFUSION | METEOROLOGY & ATMOSPHERIC SCIENCES | HAMILTONIAN DESCRIPTION | CLIMATE | Atmospheric physics | Wave propagation | Energy conservation | Dynamic meteorology | Analysis | Horizontal | Computer simulation | Mathematical analysis | Dissipation | Nonlinearity | Mathematical models | Direct power generation

global atmospheric modelling | Lorenz energy cycle | hexagonal C‐grid | Global atmospheric modelling | Hexagonal C-grid | SENSITIVITY | MODEL | FORMULATION | VORTICITY | GENERAL-METHOD | hexagonal C-grid | SCHEME | POTENTIAL ENSTROPHY | DIFFUSION | METEOROLOGY & ATMOSPHERIC SCIENCES | HAMILTONIAN DESCRIPTION | CLIMATE | Atmospheric physics | Wave propagation | Energy conservation | Dynamic meteorology | Analysis | Horizontal | Computer simulation | Mathematical analysis | Dissipation | Nonlinearity | Mathematical models | Direct power generation

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 9, pp. 3065 - 3090

A numerical scheme applicable to arbitrarily-structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector-invariant...

Potential vorticity | Voronoi diagram | C-grid | Shallow-water equations | CORES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SPHERE | OCEAN | MODEL | ALGORITHMS | PHYSICS, MATHEMATICAL | SCHEMES | Energy conservation | Analysis

Potential vorticity | Voronoi diagram | C-grid | Shallow-water equations | CORES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SPHERE | OCEAN | MODEL | ALGORITHMS | PHYSICS, MATHEMATICAL | SCHEMES | Energy conservation | Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, pp. 156 - 172

Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified...

Triangular grid | Spurious modes | Dispersion analysis | Wave propagation | Mimetic discretization | C-grid | CIRCULATION | FORMULATION | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | FLOWS | OSCILLATIONS | Noise control | Analysis | Atmospheric physics | VELOCITY | GRIDS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | FILTERS | WAVE PROPAGATION | NOISE | VISCOSITY | CONTINUITY EQUATIONS | ATMOSPHERES | ACCURACY | COMPUTERIZED SIMULATION | MATHEMATICAL SOLUTIONS | MASS

Triangular grid | Spurious modes | Dispersion analysis | Wave propagation | Mimetic discretization | C-grid | CIRCULATION | FORMULATION | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | FLOWS | OSCILLATIONS | Noise control | Analysis | Atmospheric physics | VELOCITY | GRIDS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | FILTERS | WAVE PROPAGATION | NOISE | VISCOSITY | CONTINUITY EQUATIONS | ATMOSPHERES | ACCURACY | COMPUTERIZED SIMULATION | MATHEMATICAL SOLUTIONS | MASS

Journal Article

Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 07/2009, Volume 135, Issue 642, pp. 1104 - 1116

For the shallow‐water equations on the sphere, an inherently mass‐conserving semi‐Lagrangian discretisation (SLICE) of the continuity equation is coupled with...

orographic forcing | spatial discretisation | analytical nonlinear solutions | temporal discretisation | C‐grid | Spatial discretisation | Temporal discretisation | Orographic forcing | Analytical nonlinear solutions | C-grid | SLICE | SPLINE METHOD PSM | EFFICIENT SCHEME | ADVECTION SCHEME | TEST SET | TRANSPORT PROBLEMS | CONSERVATIVE VERSION | METEOROLOGY & ATMOSPHERIC SCIENCES | ATMOSPHERIC MODELS | GEOMETRY | Nonlinearity | Mathematical models | Continuity equation | Mathematical analysis | Standards

orographic forcing | spatial discretisation | analytical nonlinear solutions | temporal discretisation | C‐grid | Spatial discretisation | Temporal discretisation | Orographic forcing | Analytical nonlinear solutions | C-grid | SLICE | SPLINE METHOD PSM | EFFICIENT SCHEME | ADVECTION SCHEME | TEST SET | TRANSPORT PROBLEMS | CONSERVATIVE VERSION | METEOROLOGY & ATMOSPHERIC SCIENCES | ATMOSPHERIC MODELS | GEOMETRY | Nonlinearity | Mathematical models | Continuity equation | Mathematical analysis | Standards

Journal Article

Ocean Modelling, ISSN 1463-5003, 05/2016, Volume 101, pp. 59 - 67

•Modified EVP (mEVP) implementation on a B-grid is more stable than on a C-grid.•On C-grids convergence of mEVP is sensitive to the discretization of the...

VP rheology | MITgcm | EVP rheology | B-grid | Sea ice | C-grid | VISCOUS-PLASTIC METHOD | OCEANOGRAPHY | MODEL | METEOROLOGY & ATMOSPHERIC SCIENCES | Atmospheric physics | Methods | Analysis | Stability | Discretization | Oceans | Mathematical analysis | Mathematical models | Computational efficiency | Convergence

VP rheology | MITgcm | EVP rheology | B-grid | Sea ice | C-grid | VISCOUS-PLASTIC METHOD | OCEANOGRAPHY | MODEL | METEOROLOGY & ATMOSPHERIC SCIENCES | Atmospheric physics | Methods | Analysis | Stability | Discretization | Oceans | Mathematical analysis | Mathematical models | Computational efficiency | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2014, Volume 273, pp. 185 - 211

We analyse several vector reconstruction methods, based on the knowledge of only specific pointwise vector components, and extend their use to non-structured...

Vector reconstruction | Staggered grid | Hybrid reconstruction method | Radial basis functions | Semi-Lagrangian | Alignment index | Wachspress spherical coordinates | Vector interpolation | Icosahedral | C grid | LARGE SETS | SPHERE | PHYSICS, MATHEMATICAL | SHALLOW-WATER MODEL | INTERPOLATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADVECTION | SURFACE | QUADRATIC SHEPARD METHOD | SCHEMES | Reconstruction | Interpolation | Least squares method | Mathematical analysis | Fields (mathematics) | Vectors (mathematics) | Computational efficiency | Transport

Vector reconstruction | Staggered grid | Hybrid reconstruction method | Radial basis functions | Semi-Lagrangian | Alignment index | Wachspress spherical coordinates | Vector interpolation | Icosahedral | C grid | LARGE SETS | SPHERE | PHYSICS, MATHEMATICAL | SHALLOW-WATER MODEL | INTERPOLATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADVECTION | SURFACE | QUADRATIC SHEPARD METHOD | SCHEMES | Reconstruction | Interpolation | Least squares method | Mathematical analysis | Fields (mathematics) | Vectors (mathematics) | Computational efficiency | Transport

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2017, Volume 339, pp. 525 - 552

A conservative discretization of the ocean primitive equations for global ocean dynamics is formulated on an unstructured grid. The grid consists of triangular...

Checkerboard pattern | Unstructured grid model | Triangular C-grid | Conservative discretization | Ocean primitive equations | Computational mode | CIRCULATION | RECONSTRUCTION | TRIANGULAR C-GRIDS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | FINITE-VOLUME | DISCRETIZATIONS | VARIABILITY | TRANSPORT | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FLOWS | Analysis | Models | Numerical analysis

Checkerboard pattern | Unstructured grid model | Triangular C-grid | Conservative discretization | Ocean primitive equations | Computational mode | CIRCULATION | RECONSTRUCTION | TRIANGULAR C-GRIDS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | FINITE-VOLUME | DISCRETIZATIONS | VARIABILITY | TRANSPORT | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FLOWS | Analysis | Models | Numerical analysis

Journal Article

Ocean Modelling, ISSN 1463-5003, 09/2013, Volume 69, pp. 64 - 78

•Triangular C-grids have “checker-board” horizontal divergence noise.•Horizontal divergence errors propagate into the vertical velocity and primary...

Horizontal divergence error | Unstructured mesh modeling | Implicit (elliptic) and explicit filtering | Secondary circulation | Triangular C-grid | FREE-SURFACE FLOWS | OCEANOGRAPHY | SEMI-LAGRANGIAN ADVECTION | MODEL | METEOROLOGY & ATMOSPHERIC SCIENCES

Horizontal divergence error | Unstructured mesh modeling | Implicit (elliptic) and explicit filtering | Secondary circulation | Triangular C-grid | FREE-SURFACE FLOWS | OCEANOGRAPHY | SEMI-LAGRANGIAN ADVECTION | MODEL | METEOROLOGY & ATMOSPHERIC SCIENCES

Journal Article

ATMOSPHERE, ISSN 2073-4433, 04/2019, Volume 10, Issue 4, p. 179

Z-grid finite volume models conserve all-scalar quantities as well as energy and potential enstrophy and yield better dispersion relations for shallow water...

Z-grid | shallow water equations | numerical efficiency | finite volume | METEOROLOGY & ATMOSPHERIC SCIENCES | stability | SHALLOW-WATER EQUATIONS | C-grid | Shallow water equations | Divergence | Velocity potential | Weather forecasting | Finite volume method | Shallow water | Variables | Energy conservation | Efficiency | Vorticity | Mathematical models | Numerical models | Integration | Stability | Climate models | Stability analysis | Velocity | Dispersion | Equations | Stream functions | Volume | Primitive equations | Enstrophy | Models | Computing time | Stencils | Time integration

Z-grid | shallow water equations | numerical efficiency | finite volume | METEOROLOGY & ATMOSPHERIC SCIENCES | stability | SHALLOW-WATER EQUATIONS | C-grid | Shallow water equations | Divergence | Velocity potential | Weather forecasting | Finite volume method | Shallow water | Variables | Energy conservation | Efficiency | Vorticity | Mathematical models | Numerical models | Integration | Stability | Climate models | Stability analysis | Velocity | Dispersion | Equations | Stream functions | Volume | Primitive equations | Enstrophy | Models | Computing time | Stencils | Time integration

Journal Article

Monthly Weather Review, ISSN 0027-0644, 2008, Volume 136, Issue 6, pp. 2112 - 2119

The NCAR Community Climate System Model (CCSM) finite-volume atmospheric core uses a C-D-grid discretization to solve the equations of motion. A linear...

ADVECTION SCHEMES | STABILITY | CORIOLIS TERMS | EQUATIONS | C-GRID MODELS | SIMULATION | METEOROLOGY & ATMOSPHERIC SCIENCES | Atmospheric models | Reverse engineering | Velocity | Meteorology

ADVECTION SCHEMES | STABILITY | CORIOLIS TERMS | EQUATIONS | C-GRID MODELS | SIMULATION | METEOROLOGY & ATMOSPHERIC SCIENCES | Atmospheric models | Reverse engineering | Velocity | Meteorology

Journal Article

Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, 2/2014, Volume 28, Issue 1, pp. 107 - 128

We demonstrate how efficient r-adapted grids for the prediction of tropical cyclone (TC) tracks can be constructed with the help of goal-oriented error...

Engineering | Geophysical shallow-water equations | Hexagonal C-grid model | A posteriori error estimation | Engineering Fluid Dynamics | Goal-oriented r-adaptivity | Binary tropical cyclone interaction | Computational Science and Engineering | Classical Continuum Physics | GRIDS | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | SENSITIVITY | BAROTROPIC MODEL | PREDICTION | MECHANICS | MOTION | SCALE VORTICES | SYSTEMS | Hydrofoil boats | Tropical cyclones | Vortex-motion | Mathematical research | Hydrodynamics | Models | Research | Error analysis (Mathematics) | Studies | Cyclones | Error analysis | Fluid dynamics | Vortices | Permissible error | Errors | Accuracy | Algorithms | Computational fluid dynamics | Mathematical models | Estimates

Engineering | Geophysical shallow-water equations | Hexagonal C-grid model | A posteriori error estimation | Engineering Fluid Dynamics | Goal-oriented r-adaptivity | Binary tropical cyclone interaction | Computational Science and Engineering | Classical Continuum Physics | GRIDS | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | SENSITIVITY | BAROTROPIC MODEL | PREDICTION | MECHANICS | MOTION | SCALE VORTICES | SYSTEMS | Hydrofoil boats | Tropical cyclones | Vortex-motion | Mathematical research | Hydrodynamics | Models | Research | Error analysis (Mathematics) | Studies | Cyclones | Error analysis | Fluid dynamics | Vortices | Permissible error | Errors | Accuracy | Algorithms | Computational fluid dynamics | Mathematical models | Estimates

Journal Article

Applied Mechanics and Materials, ISSN 1660-9336, 05/2012, Volume 170-173, pp. 2248 - 2255

A two dimensional semi-implicit finite volume free-surface ocean model(FVFOM2D) based on unstructured C-grid is built, in which the momentum equation is...

Finite volume method | Coastal ocean modeling | Unstructured C-grid

Finite volume method | Coastal ocean modeling | Unstructured C-grid

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2011, Volume 32, Issue 4, pp. 1475 - 1499

We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady...

saddle point problem | incompressible (Navier-)Stokes equations | constraint preconditioning | PERFORMANCE | ALGORITHM | DECOMPOSITION | Arakawa C-grid | FLOW | incomplete factorization | F-matrix | electrical networks | PRECONDITIONERS | NAVIER-STOKES EQUATIONS | ILU | SYSTEMS | grid-independent convergence | indefinite matrix | Grid-independent convergence | Incomplete factorization | Saddle point problem | Incompressible (Navier-)Stokes equations | Indefinite matrix | Electrical networks | Constraint preconditioning | MATHEMATICS, APPLIED | Data- och informationsvetenskap | Computer and Information Sciences | Naturvetenskap | Natural Sciences

saddle point problem | incompressible (Navier-)Stokes equations | constraint preconditioning | PERFORMANCE | ALGORITHM | DECOMPOSITION | Arakawa C-grid | FLOW | incomplete factorization | F-matrix | electrical networks | PRECONDITIONERS | NAVIER-STOKES EQUATIONS | ILU | SYSTEMS | grid-independent convergence | indefinite matrix | Grid-independent convergence | Incomplete factorization | Saddle point problem | Incompressible (Navier-)Stokes equations | Indefinite matrix | Electrical networks | Constraint preconditioning | MATHEMATICS, APPLIED | Data- och informationsvetenskap | Computer and Information Sciences | Naturvetenskap | Natural Sciences

Journal Article

Ima journal of numerical analysis, ISSN 0272-4979, 01/2009, Volume 29, Issue 1, pp. 208 - 234

We present a new algorithm that constructs a fill-reducing ordering for a special class of saddle point matrices: the F-matrices. This class contains the...

PRECONDITIONERS | NAVIER-STOKES EQUATIONS | TREES | LINEAR-EQUATIONS | SPARSE | SYMMETRIC INDEFINITE SYSTEMS | ELIMINATION | DEGREE ORDERING ALGORITHM | ℱ-matrix | (Navier-)Stokes equations | Saddle point problem | Indefinite matrix | Electrical networks | Factorization | Numerical stability | C-grid | Growth factor | MATHEMATICS, APPLIED | SYSTEMS | ALGORITHMS

PRECONDITIONERS | NAVIER-STOKES EQUATIONS | TREES | LINEAR-EQUATIONS | SPARSE | SYMMETRIC INDEFINITE SYSTEMS | ELIMINATION | DEGREE ORDERING ALGORITHM | ℱ-matrix | (Navier-)Stokes equations | Saddle point problem | Indefinite matrix | Electrical networks | Factorization | Numerical stability | C-grid | Growth factor | MATHEMATICS, APPLIED | SYSTEMS | ALGORITHMS

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2006, Volume 211, Issue 1, pp. 210 - 228

Fully-implicit primitive equation ocean models are useful to study the sensitivity of steady ocean flows to parameters, to determine bifurcations of these...

Fourier analysis | Geophysical flow | Implicit B-grid model | Implicit C-grid model | Wiggles | PLANETARY-WAVES | CIRCULATION | geophysical flow | wiggles | implicit B-grid model | implicit C-grid model | FLOWS | BUOYANCY FORCES | ADJUSTMENT | SHALLOW-WATER EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Meteorological research | Analysis | Models

Fourier analysis | Geophysical flow | Implicit B-grid model | Implicit C-grid model | Wiggles | PLANETARY-WAVES | CIRCULATION | geophysical flow | wiggles | implicit B-grid model | implicit C-grid model | FLOWS | BUOYANCY FORCES | ADJUSTMENT | SHALLOW-WATER EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Meteorological research | Analysis | Models

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 7, pp. 2706 - 2721

C-grid discretizations based on a hexagonal or triangular mesh can be investigated with the help of a planar trivariate coordinate system, where the vector...

Shallow water equations | C-grid | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSTROPHIC ADJUSTMENT | MODELS | DYNAMICS | SPHERICAL GEOMETRY | PHYSICS, MATHEMATICAL | Reconstruction | Divergence | Discretization | Mathematical analysis | Mathematical models | Decomposition | Vectors (mathematics)

Shallow water equations | C-grid | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSTROPHIC ADJUSTMENT | MODELS | DYNAMICS | SPHERICAL GEOMETRY | PHYSICS, MATHEMATICAL | Reconstruction | Divergence | Discretization | Mathematical analysis | Mathematical models | Decomposition | Vectors (mathematics)

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2016, Volume 310, pp. 127 - 160

Many newly developed climate, weather and ocean global models are based on quasi-uniform spherical polygonal grids, aiming for high resolution and better...

Staggered C grid | Finite volume | Spherical Voronoi grid | Shallow water model |

Staggered C grid | Finite volume | Spherical Voronoi grid | Shallow water model |