Modeling global ocean circulation on unstructured meshes: current status and perspectives

S. Danilov, Q. Wang, D. Sidorenko, J. SchröterAlfred Wegener Institute, Bremerhaven, Germany

Goal: Modelling large-scale ocean circulation

Main motivation: Representation of coastlines, straits, or need to resolve local processes will benefit from using variable resolution

Existing models: ADCIRC, TELEMAC, FVCOM, UnTRIM, ... main area – coastal oceanography FEOM/FESOM (AWI) – large-scale circulation

SLIM (University Louvain la Neuve), ICOM (Imperial)

As a rule the complex shape of ocean basin requires to invest degreesof freedom in geometry => low-order elements are used

What we have already triedin FEOM

P1-P1 version(3D primitive equations)

Current versions:prismatic and tetrahedral P1-P1

Prismatic:more symmetric verticalstencilquadratures on generalizedmeshes (slow)

Tetrahedra: implementation of generalized vertical coordinate is straightforward

inclined vertical stencil

Main features:Pressure(elevation) correction method (no barotropic velocity)Explicit (where possible)TG, FCT (TG-based) and GLS-stabilized advection schemes.Nonlinear free surface and nonhydrostatic options MPI parallelized, coupled to sea ice, realistic forcing (CORE)Examples – D. Sidorenko talk

Main difficulties:Implicit vertical viscosity/diffusion is slow because of horizontal connections in CG Slope noise in GM in tetrahedral discretizationDifficult to keep pressure and vertical velocity fully consistent

In hydrostatic finite-element codes:elevation, w, tracers, and pressure should have the same horizontal discretization. w, pressure and density - same vertical discretization=> Consistent w/p solution is difficult to obtain with CG tracers!

CPU time: prismatic and tetrahedral codes behave very similar:Despite 3 times larger amount of elements each of them is less CPU-expensive.

Q. Wang

Ross Sea overflow, simulations by Q. Wang. Resolution 0.5 km – 30 km

P1nc-P1 branchPressure correction method (without stabilization).Tracer part inherited from FEOM

Advantages: no stabilizationDiagonal mass matrix forvelocity (on z-meshes) .Difficulty: momentumadvection (P1 re-projectionis much more robust than trueP1nc)

Intercomparison between P1-P1P1nc-P1 versions of FEOM andMITgcm suggests that NC version is marginally faster(about 10%); FEOM is about 10 times slower than MITgcm

Temperature distribution in 1/6degree, 16 layers channel after3 years of evolution (100 m)

Kinetic energy evolution ina baroclinically unstablechannel flow

P1nc-P1: further developments

Lon-lat free version (following ideas of Louvain group)Velocity: P0 in vertical (more consistent boundary conditions on z-coordinate meshes)

CPU speed remains our major difficulty as our typical applications require weeks to be completed on available resources (64-256 cores).

FV technologies have to be explored.

FV type of discretization (an analog of P0-P1; velocity vector at centroids,scalar fields – at nodes)

Although scalar control volumes (dual median) look ugly, assembling RHSs is fast using the edge-based structure.

Pressure (elevation) correction (semi-implicit), AB2 Coriolis,Implicit vertical diffusion, z-levels. Momentum and tracer advection is second-order (linear reconstruction) upwind.

Main result: Compared to P1-P1 approach the code is a factor from 5 to 8 faster!

NA setup with focus on theGulf Stream (1/5 degree), coarseotherwise.Total 0.7M 3D nodes.Time step 20 min, 1 year takesabout 3 h on a single node (8 Power5 1.9 GHz processors) of IBM p575

Seemingly too diffusive traceradvection (upwind with linear reconstruction).

Snapshot of pot. temperature at 175 m

Sea surface elevation

Vertical velocity patterns:A very consistent global structureon coarse mesh and noisy pattern in well-resolved strong jetsand eddies.Suppressing it is easy butaffects dynamics.

Resolving eddies brings about much stronger and noisy local vertical velocities than on coarse grids.

Summary of FV approach:

(i) Much faster than P1-P1.

(ii) Requires better advection schemesfor both momentum and tracer advectionin eddy-resolving applications. There is no easy way of reaching this.

Spurious diapycnal mixing: Baroclinic instability in a channel

Anomaly of sorted densityDiagnosed mixing

1. Spurious mixing in FEOM advectionscheme is not larger than in finite difference models as compared to Griffies et al., 2000.

2. FV 2nd order upwind advection scheme shows large dissipation and must be improved before it can be used in large scale ocean modelling.

3. Unstructured character of meshes does not necessarily imply increased mixing.

Some conclusions:P1-P1 setup is most robust (of tested by us) and allows us to run variousapplications at the current stage.

FV approach suggests much higher CPU efficiency, however applying it toeddying regimes requires care with respect to advection schemes and dissipation operators.

There are many promising element pairs, and there are many indications in favor of DG. How can we ensure a practical (sufficiently fast) approach?