Non-hydrostatic algorithm and dynamics in ROMS Yuliya Kanarska, Alexander Shchepetkin, Alexander...
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- Slide 1
- Non-hydrostatic algorithm and dynamics in ROMS Yuliya Kanarska,
Alexander Shchepetkin, Alexander Shchepetkin, James C. McWilliams,
IGPP, UCLA
- Slide 2
- UCLA ROMS UCLA ROMS A parallel three-dimensional numerical
oceanic model in vertical hybrid z-sigma and horizontal curvilinear
coordinates with innovative algorithms for advection, mixing,
pressure gradient, vertical-mode coupling, time stepping
(Shchepetkin and McWilliams, 1998, 2003, 2005) Non-hydrostatic
capabilities (2005)
- Slide 3
- Where are non-hydrostatic effects important? steep waves on
uneven bottom in coastal areas unbalanced flows, baroclinic
barotropic instability steepening, breaking of internal waves of
large amplitude generated by the tidally driven flows over steep
topography steepening, breaking of internal waves of large
amplitude generated by the tidally driven flows over steep
topography gravity currents gravity currents deep convection in the
open ocean deep convection in the open ocean.
- Slide 4
- Hydrostatic approximation: Governing Equations H/L
- Barotropic mode Pressure correction step Tracers Provisional
velocity field tracers (n-2,n-1,n,n+1) AM4 interpolation =>
momentum (n-2,n-1,n) AB3 extrapolation (n-2,n-1,n,n+1) AM4
interpolation
- Slide 11
- Barotropic mode Pressure correction step Tracers Provisional
velocity field tracers (n-2,n-1,n,n+1) AM4 interpolation =>
momentum (n-2,n-1,n) AB3 extrapolation (n-2,n-1,n,n+1) AM4
interpolation
- Slide 12
- Non-hydrostatic algorithm for ROMS model Non-hydrostatic
algorithm for ROMS model Components Components pressure
decomposition on hydrostatic, non- hydrostatic (nh) terms pressure
correction method for nh pressure mode splitting on barotropic and
baroclinic components with explicit free surface treatment
Algorithm Algorithm includes non-hydrostatic terms in both
barotropic and baroclinic modes guarantees mass conservation
properties and agreement between modes at each discrete time
step
- Slide 13
- What new regarding boundary conditions in nh setup? Momentum
equation and time splitting for w Kinematical boundary conditions
for vertical velocity: Boundary conditions for velocity field are
satisfied before correction step => Boundary conditions for
velocity field are satisfied before correction step => Neumann
conditions for q at rigid boundaries; Neumann conditions for q at
rigid boundaries; q=0 at free surface. q=0 at free surface..
- Slide 14
- Poisson equation in curvilinear - coordinate system L: L: 15
diagonal; non-symmetric; inseparable in horizontal and vertical
directions inseparable in horizontal and vertical directions
- Slide 15
- MPI Massively parallel Elliptic solvers of large sparse matrix
PETSC (Argonne National Laboratory) PETSC (Argonne National
Laboratory) HYPRE (Lawrence Livermore National Laboratory) HYPRE
(Lawrence Livermore National Laboratory) ? ?
- Slide 16
- HYPRE (Solvers and Preconditioners) HYPRE (Solvers and
Preconditioners) MPI domain portioning approach in the same way as
in ROMS (in xy-plane) no decomposition in z-direction; Using
Structured grid interface of HYPRE
- Slide 17
- Preliminary results of the HYPRE implementation in ROMS CG
GMRES SMG PFMG CG+SMG CG+ PFMG CG SMG PFMG CG+SMG CG+ PFMG
200x50x50 test case 100x100x100 test case 200x50x50 test case
100x100x100 test case (internal seiche waves in rectangular basin)
(standing barotropic waves in deep basin) Testing of different
solvers and preconditioners for 1 (red) and 4 (blue) processors
Multigrid converges quickly (1-4) iterations but requires
significant execution time per iteration; Krylov methods (CG,
GMRES) converges for ~ 20 iterations but even for that number
iterations generally it works faster; Krylov methods with multigrid
as preconditioner converges very quickly (1-5 iteration) and it is
quite efficient
- Slide 18
- Internal seiche gravity waves simulations Horn et al. 2000
experiment
- Slide 19
- Hydrostatic vs. non-hydrostatic simulations with ROMS
Hydrostatic Non-hydrostatic pressure distribution
- Slide 20
- Interface displacement in the center of tank
- Slide 21
- Standing surface waves in deep basin U-non-hydrostatic
U-hydrostatic W-non-hydrostatic Non-hydrostatic pressure correction
Dispersion relation Free surface oscillations
- Slide 22
- Density distribution in hydrostatic simulations KH baroclinic
instability Density distribution in non-hydrostatic simulations Nh
pressure correction Hydrostatic stable time step two times smaller
then non-hydrostatic!
- Slide 23
- NLIW generation by interaction of barotropic tide with sill
Dimensionless parameters Luzon strait sill: supercritical finite
depth topography
- Slide 24
- Strong barotropic tide Temperature (C) U-velocity (cm/s)
Non-hydrostatic pressure L=600 km H=2.5 km L SILL =80 km H SILL
=1.8 km Resolution 2D 800x5x80
- Slide 25
- HydrostaticNon-Hydrostatic Temperature (C) U-velocity
(cm/s)
- Slide 26
- Bernsten J., Furnes G. (2005) Internal pressure errors in sigma
coordinate ocean models- sensitivity of the growth of the flow to
the time stepping method and possible non-hydrostatic effects
Non-hydrostatic -error ROMS simulations with pressure-gradient
Scheme (Shchepetkin, McWilliams 2003) Kinetic energy for seamount
test
- Slide 27
- Future ROMS NH Algorithm Directions Further optimization of
elliptic solver; Further optimization of elliptic solver;
Optimization of the calculations of cross-derivatives terms in
pressure equation; Optimization of the calculations of
cross-derivatives terms in pressure equation; Simulations in
complex domains and convergence testing; Simulations in complex
domains and convergence testing; Studies and testing for larger
number of processors and highly resolution problems. Studies and
testing for larger number of processors and highly resolution
problems.