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Tolosa Documentation

Tolosa-lct Presentation

Tolosa-lct (Leucothea) is a Boussinesq-type dispersive wave solver for phase-resolved coastal wave modeling on unstructured meshes with CPU MPI parallelism. It implements a novel hyperbolized Green-Naghdi model that extends Tolosa-sw with non-hydrostatic pressure, vertical velocity, dispersive effects, wave breaking via enstrophy, and active wave generation. It is built on the Tolosa-lib library and developed at IMT Toulouse (INSA/CNRS & SHOM).

Governing Equations

Section titled “Governing Equations”

Tolosa-lct extends the shallow water equations via an acoustic splitting. The base system has 5 scalar unknowns : water depth, depth-averaged horizontal velocity (2D vector), depth-averaged vertical velocity, and acoustic (non-hydrostatic) pressure. When compiled with USE_DISP=yes, a strain-like vector is added, bringing the system to 7 scalar unknowns and improving dispersion to Padé (2,2) accuracy. A scalar enstrophy (wave_break_model=2) can be added to model wave breaking.

  • Acoustic part: the sub-system drives dispersive wave propagation at speed ; sub-iterated at each Saint-Venant time step with Mach number .
  • Bathymetric corrections: terms in , , that remove the mild slope assumption, where and are material derivatives of the bathymetry and its gradient. For fixed bathymetry , so .
  • Augmented model: the strain-like vector improves the dispersion relation to Padé (2,2) accuracy when .
  • Wave breaking: enstrophy variable measures local turbulence intensity; turbulent viscosity with controlling turbulence intensity and the dissipation rate; activated by wave_break_model=2.

Dispersion relation (linear waves, flat bottom):

Total energy:

Supported Physics

Section titled “Supported Physics”
  • Non-hydrostatic dispersion — acoustic splitting at a prescribed Mach number; local or global acoustic speed; energy-dissipating Lax-Wendroff-like scheme for (w, p) sub-stepping; configurable tapering near wet/dry interfaces
  • Wave maker / active generation — spectral wave forcing (wave BC type); ALE active generation (ale(L)#user#tag, requires ALE=yes); sponge/relaxation zones for simultaneous wave generation and outgoing absorption
  • Wave breaking — two models:
    • Symphonie-NH (wave_break_model=1): viscosity-based breaker detection and momentum dissipation
    • Enstrophy-based (wave_break_model=2): dissipation with Iribarren-number criterion and an original enstrophy variable measuring local turbulence
  • Bottom friction — three models (oceanic, oceanic with log-law, Manning/Strickler), all supporting spatially variable coefficients
  • Coriolis — Crank-Nicolson semi-implicit; from latitude file or beta-plane
  • Open boundary conditions — wall, neumann, q, ssh, tide, ssht, wave, wave/ssht, wave/tide, relaxation zones (r, rssh, sshs), ALE generation (ale)
  • SSH boundary forcing (ssht) — time-interpolated per boundary edge
  • Tidal body force — gravitational tidal potential per constituent; applied to momentum at interval dt_tbf
  • Wind stress — from time-interpolated binary files
  • Atmospheric pressure — ; optional inverse barometer correction at open boundaries

Operational Use Cases

Section titled “Operational Use Cases”

Île de Ré

Section titled “Île de Ré”
  • Mesh of ~11 M cells
  • JONSWAP wave spectrum boundary conditions, peak frequency 0.1 Hz with directional spreading
  • Relaxation zones on outgoing directions
  • Pseudo-breaking with adaptive friction near beaches

Saint-Malo

Section titled “Saint-Malo”
ConfigurationDescription
Low-res~1 M cells, JONSWAP spectrum, 20-min simulation on a MacBook Pro M2
High-res~16 M cells for ~50 km², resolution from 1 m at coast to 3.5 m offshore

Both configurations use JONSWAP spectra with directional spreading and relaxation boundary conditions.

Performance

Section titled “Performance”

Computational cost: 3–5× the Saint-Venant solver for equivalent domains
(~10 min / 1 h of physical time / 10⁶ mesh cells / modern CPU node).

Good MPI scaling on CPU and GPU architectures — see HPC Performance.

Next Steps

Section titled “Next Steps”