Reconciling estimates of the free surface height in Lagrangian vertical coordinate ocean models with mode-split time stepping

2009 ◽  
Vol 29 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Robert Hallberg ◽  
Alistair Adcroft
Keyword(s):  
Free Surface ◽  
Vertical Coordinate ◽  
Time Stepping ◽  
Mode Split ◽  
Ocean Models ◽  
Split Time ◽  
Split Time Stepping

scholarly journals WAVETRISK-2.1: an adaptive dynamical core for ocean modelling

2021 ◽  
Author(s):  
Nicholas Keville-Reynolds Kevlahan ◽  
Florian Lemarié
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Time Integration ◽  
Ocean Model ◽  
Mesh Adaptivity ◽  
Time Step ◽  
Vertical Coordinate ◽  
Slip Boundary ◽  
Modelling Framework ◽  
Atmosphere Model

Abstract. This paper introduces WAVETRISK-2.1 (i.e. WAVETRISK-OCEAN), an incompressible version of the atmosphere model wavetrisk-1.x with free-surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses DYNANICO's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic--baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth-system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties.

scholarly journals Achieving Seventh-Order Amplitude Accuracy in Leapfrog Integrations

2013 ◽  
Vol 141 (9) ◽  
pp. 3037-3051 ◽  
Author(s):  
Paul D. Williams
Keyword(s):  
Nonlinear System ◽  
Third Order ◽  
First Order ◽  
Time Stepping ◽  
The Third ◽  
Numerical Integrations ◽  
Seventh Order ◽  
Ocean Models ◽  
Stability And Accuracy ◽  
Fifth Order

Abstract The leapfrog time-stepping scheme makes no amplitude errors when integrating linear oscillations. Unfortunately, the Robert–Asselin filter, which is used to damp the computational mode, introduces first-order amplitude errors. The Robert–Asselin–Williams (RAW) filter, which was recently proposed as an improvement, eliminates the first-order amplitude errors and yields third-order amplitude accuracy. However, it has not previously been shown how to further improve the accuracy by eliminating the third- and higher-order amplitude errors. Here, it is shown that leapfrogging over a suitably weighted blend of the filtered and unfiltered tendencies eliminates the third-order amplitude errors and yields fifth-order amplitude accuracy. It is further shown that the use of a more discriminating (1, −4, 6, −4, 1) filter instead of a (1, −2, 1) filter eliminates the fifth-order amplitude errors and yields seventh-order amplitude accuracy. Other related schemes are obtained by varying the values of the filter parameters, and it is found that several combinations offer an appealing compromise of stability and accuracy. The proposed new schemes are tested in numerical integrations of a simple nonlinear system. They appear to be attractive alternatives to the filtered leapfrog schemes currently used in many atmosphere and ocean models.

Comparisons of Two Different Mixed Eulerian-Lagrangian Schemes Based on a Study of Flare-Slamming Hydrodynamics

1996 ◽  
Vol 118 (3) ◽  
pp. 174-183
Author(s):  
M. L. Wang ◽  
A. W. Troesch ◽  
B. Maskew
Keyword(s):  
Free Surface ◽  
Comparative Study ◽  
Numerical Simulations ◽  
Fourier Coefficients ◽  
Fully Nonlinear ◽  
Time Stepping ◽  
Time Histories ◽  
Nonlinear Free Surface ◽  
Simulated Time ◽  
Flare Slamming

A comparative study of two different mixed Eulerian-Lagrangian methods is presented. Representative numerical simulations of oscillatory flare-slamming flows are given. Computations based on these two different numerical schemes, i.e., a desingularized method using Rankine ring sources and a source-doublet panel method (e.g., USAERO/FSP©), are compared with experiments. Fourier coefficients of the simulated time histories and experimentally measured forces are given for detailed error comparisons. The numerical simulations demonstrate the ranges of applicability of these two methods. Both are shown to be efficient and robust time-stepping schemes for the fully nonlinear free-surface problem studied here.

On Two Alternative Field Solutions for Second-Order Wave Diffraction

1991 ◽  
Vol 113 (3) ◽  
pp. 185-192 ◽  
Author(s):  
K. F. Cheung ◽  
M. Isaacson
Keyword(s):  
Free Surface ◽  
Nonlinear Boundary ◽  
Series Representation ◽  
Taylor Series Expansion ◽  
Perturbation Series ◽  
Two Dimensions ◽  
Second Order ◽  
Alternative Methods ◽  
Time Stepping ◽  
Alternative Field

The present paper set out a nonlinear boundary value problem involving the interaction of surface waves with large submerged structures in two dimensions. The problem is solved to second order by a time-stepping procedure on the basis of two alternative methods. Both of these involve the application of Green’s theorem, a Taylor series expansion of variables at the free surface and a perturbation series representation of the pertinent variables. Differences between the two solutions are associated with alternative integral equations applicable to second-order terms. The two second-order solutions are compared with each other and with previous theoretical and experimental results, and their applicability is assessed.

WAVETRISK-OCEAN: an adaptive dynamical core for ocean modelling

2021 ◽  
Author(s):  
Kevlahan Nicholas
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Time Integration ◽  
Ocean Model ◽  
Time Step ◽  
Vertical Coordinate ◽  
Modelling Framework ◽  
Standard Set ◽  
Atmosphere Model ◽  
Multilayer Shallow Water Equations

<p>This talk introduces WAVETRISK-OCEAN, an incompressible version of the atmosphere model WAVETRISK.  This new model is built on the same wavelet-based dynamically adaptive core as WAVETRISK, which itself uses DYNAMICO's mimetic vector-invariant multilayer shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping.  The ocean variant solves the incompressible multilayer shallow water equations with a Ripa type thermodynamic treatment of horizontal density gradients.  Time integration uses barotropic-baroclinic mode splitting via an implicit free surface formulation, which is about 15 times faster than explicit time stepping.  The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization.  Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount,  upwelling and baroclinic jet) as well as  turbulent wind-driven gyre flow in simplified geometries.  An innovative feature of WAVETRISK-OCEAN is that it could be coupled easily to the WAVETRISK atmosphere model, providing a simple integrated Earth system model using a consistent modelling framework.</p>

scholarly journals A method for applying lateral surface eddy diffusion in ocean models with a general vertical coordinate

2021 ◽  
Author(s):  
Gustavo M. Marques ◽  
Andrew E. Shao ◽  
Scott D. Bachman ◽  
Gokhan Danabasoglu ◽  
Frank O. Bryan
Keyword(s):  
Lateral Surface ◽  
Eddy Diffusion ◽  
Vertical Coordinate ◽  
Ocean Models
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