Click here to load reader
Upload
delftsoftwaredays
View
339
Download
5
Embed Size (px)
DESCRIPTION
SWAN Advanced Course
Citation preview
SWAN Advanced Course4. Numerics in SWAN
Delft Software Days28 October 2014, Delft
Contents
• Discretization
• Convergence criteria
• Source term stability
2
Discretization
• Numerical schemes for propagation (fully implicit):
• x,y-space : upwind: BSBT (1st order), SORDUP (2nd),Stelling-Leendertse (3rd)
• time : backward• -space : hybrid central / upwind (first order upwind too
diffusive, central scheme prone to wiggles)• -space : hybrid central / upwind
• Implicit propagation scheme is unconditionally stable: robust• 1st order scheme is rather diffusive (take care on large distances)• accuracy = f ( t, x, y, , )• iterative (4 sweep) solution technique• x,y-space: regular, curvi-linear or unstructured grids
3
Propagation (x,y-space)
• To allow for energy crossing the quadrants (refraction,quads, diffraction):
• Iterative procedure
• Computation is stopped when accuracy criteria are met(specified by user)
4
Convergence if:
a.
b.
c. Conditions a. AND b. are satisfied in 98% of all wet grid points
Lake George:
2% criteria vs.fully-converged
Convergence criteria
( ) ( ) ( ) ( )0 0 0 0or0.02 0.02i i i average
m m m mH H H H( ) ( ) ( ) ( )01 01 01 01or0.02 0.02i i i average
m m m mT T T T
5
Convergence criteria
Hs
DHSIGN
90%-conv. crit.
default 98%-conv. crit.
Hs
Example: 2003 experiment NCEX(Levi Gorrell)
6
• Check iteration behaviour of output quantities
• TEST output
• DHS, DRTM01
• Default not always effective significant inaccuracies
• Either stronger accuracy than default (2%) or use differentconvergence criterium: based on curvature
Convergence criteria
7
Convergence criteria
Curvature-based convergence criteria (Zijlema & vd Westhuysen 2005)
0 0( ) / [ . m a x ]ii i m mH H curv
1 10 0 0 0
1 10 0
,i i i im m m m
i im m
H H T T drelH T
and
Haringvliet Estuary Lake George
in more than [npnts] % of wet points
8
Convergence enhancing measures
HF waves have much shorter time scales than LF waves AN=b stiff
Mismatch additional measures required
Economically, large computational time steps
( )gN c N S Et
N bA
Many time scales are involved in evolution of wind waves
9
Convergence enhancing measures
This may lead to numerical instabilities. Two solutions:
1. Action density limiter:restriction of the total change of action density per iteration ateach wave component
2. Under relaxation
32PM
g
Nk c Phillips equilibrium spectrum
0.1
10
2. Under-relaxation: enhancing main diagonal stabilizing effect
11,
i iiN N AN b
1i iA I N b N
• Under-relaxation improves iteration behaviour
• Under-relaxation slows convergence
• Not meaningful for nonstationary computations
Convergence enhancing measures
- pseudo timestep -> smaller updates N- costs computational time- frequency dependent- alfa to be set in swan input file (0.002-0.01)
11
Hm0 deep water, fetch = 12.5 km
0.1
U10 = 10 m/s
U10 = 30 m/s
Convergence enhancing measures
• Effect limiter is clear withoutunder-relaxation
• Under-relaxation improvesiterative behaviour:
• Smoothed
• Reduction of overshoot
• Alteration of limiter activity
• Under-relaxation slowsconvergence
12
• Boundary conditions where waves enter computational domain• Measured / computed 2D spectra• Nesting of SWAN runs• Nesting with course-grid WAM or WAVEWATCH run
Procedure:1. Available spectra are normalized first by mean frequency and
direction2. Linear interpolation of spectra in intermediate locations3. Resulting spectra are transformed back
Interpolation
13
(Bi-linear) interpolation of input grids on computational grid :• Bathymetry• Wind field• Current field• Water level field• Bottom friction
Interpolation
WARNINGS:• Resolve relevant spatial and temporal details• Input grid should cover computational grid entirely• Bottom: input grid ~ computational grid
14
And also:
MXITST=0 is useful for checking the input!
15