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# DSD-INT - SWAN Advanced Course - 04 - Numerics in SWAN

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### DSD-INT - SWAN Advanced Course - 04 - Numerics in SWAN

1. 1. SWAN Advanced Course 4. Numerics in SWAN Delft Software Days 28 October 2014, Delft
2. 2. Contents • Discretization • Convergence criteria • Source term stability 2
3. 3. Discretization • Numerical schemes for propagation (fully implicit): • x,y-space : upwind: BSBT (1st order), SORDUP (2nd), Stelling-Leendertse (3rd) • time : backward • V-space : hybrid central / upwind (first order upwind too diffusive, central scheme prone to wiggles) • T-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, 'V, 'T) • iterative (4 sweep) solution technique • x,y-space: regular, curvi-linear or unstructured grids 3
4. 4. 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
5. 5. Convergence criteria Lake George: 2% criteria vs. fully-converged Convergence if: a. 'H ( i ) 0.02 H ( i ) or 'H ( i ) 0.02 H ( average ) m 0 m 0 m 0 m 0 b. 'T () i 0.02 T () i or 'T () i 0.02 T ( average ) m 01 m 01 m 01 m 01 c. Conditions a. AND b. are satisfied in 98% of all wet grid points 5
6. 6. Convergence criteria Hs DHSIGN 90%-conv. crit. default 98%-conv. crit. Hs Example: 2003 experiment NCEX (Levi Gorrell) 6
7. 7. Convergence criteria • Check iteration behaviour of output quantities • TEST output • DHS, DRTM01 • Default not always effective o significant inaccuracies • Either stronger accuracy than default (2%) or use different convergence criterium: based on curvature 7
8. 8. Convergence criteria Curvature-based convergence criteria (Zijlema vd Westhuysen 2005) i i i i m m m m 1 1 H H T T drel H T ' ( ' H ) / H i [ cur v .ma x ] and 0 0 , 0 0 @ i i m 0 m 0 i i m m 1 1 0 0 in more than [npnts] % of wet points Haringvliet Estuary Lake George 8
9. 9. Convergence enhancing measures N c N S E t ( ) g ª º ª º ª º « » « » « » « » « » « » «¬ »¼ «¬ »¼ «¬ »¼ HF waves have much shorter time scales than LF waves Æ AN=b stiff Mismatch Î additional measures required Economically, large computational time steps w  w N b A % % Many time scales are involved in evolution of wind waves 9
10. 10. 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 at each wave component D PM 2 3 2. Under relaxation g N k c J V ' J 0.1 Phillips equilibrium spectrum 10
11. 11. Convergence enhancing measures 2. Under-relaxation: enhancing main diagonal Æ stabilizing effect G G G G N i N i 1 ANi b , W 1 DV W - pseudo timestep Ĳ - smaller updates N - costs computational time - frequency dependent - alfa to be set in swan input file (0.002-0.01) G G G ADV I
12. 12. Ni b DV Ni1 • Under-relaxation improves iteration behaviour • Under-relaxation slows convergence • Not meaningful for nonstationary computations 11
13. 13. Convergence enhancing measures Hm0 deep water, fetch = 12.5 km J 0.1 U10 = 10 m/s U10 = 30 m/s • Effect limiter is clear without under-relaxation • Under-relaxation improves iterative behaviour: • Smoothed • Reduction of overshoot • Alteration of limiter activity • Under-relaxation slows convergence 12
14. 14. Interpolation • 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 direction 2. Linear interpolation of spectra in intermediate locations 3. Resulting spectra are transformed back 13
15. 15. Interpolation (Bi-linear) interpolation of input grids on computational grid : • Bathymetry • Wind field • Current field • Water level field • Bottom friction WARNINGS: • Resolve relevant spatial and temporal details • Input grid should cover computational grid entirely • Bottom: input grid ~ computational grid 14
16. 16. And also: MXITST=0 is useful for checking the input! 15