Boundary Conditions

Assigning BC Types

Cartesian meshes — four sides set via input.txt:

bc_N = wall
bc_S = wall
bc_W = neumann
bc_E = ssh#1.5

Gmsh meshes — the BC type is the name of the physical group in the .msh file. For types that require data, the string is also used as the file name stem (e.g. physical group inlet → file bc_inlet.txt).

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BC Types Reference

Tolosa-lct extends the Tolosa-sw BC types with wave maker and relaxation zone conditions:

Type	Prescribes	computation	Required input
wall	—	(reflection)	—
neumann	—	(zero gradient)	—
periodic	—	coupled to opposite boundary	—
q	constant discharge	from prescribed	tag q#value or bc_<name>.txt
q(t)	time-varying discharge	same	bc_<name>.txt
ssh	constant		tag ssh#value, bc_user(), or bc_<name>.txt
ssh(t)	time-varying	same	bc_<name>.txt
h	constant depth	same as ssh	tag h#value, bc_user(), or bc_<name>.txt
h(t)	time-varying depth	same	bc_<name>.txt
ratcurve	stage–discharge table	from table	bc_<name>.txt
tide	from tidal harmonics	same as ssh	tide.list + forcing.<name>tide.a/.b
ssht	from spatially-varying time series	same as ssh	ssht_edge_at_bc.a/.b
ssht/tide		same as ssh	all of the above
wave	spectral wave maker from file	from wave spectrum	forcing.wave_spectrum.a/.b
wave/ssht	wave maker + ssht	same	forcing.wave_spectrum.a/.b + ssht_edge_at_bc.a/.b
wave/tide	wave maker + tidal harmonics	same	forcing.wave_spectrum.a/.b + tide.list
wave/ssht/tide	wave maker + ssht + tide	same	all of the above
r(L)#user#tag	sponge/relaxation zone, length L	smooth transition to bc_user() over distance L	bc_user()
rssh#η#L	sponge relaxation toward constant	same	inline values
sshs(L)#user#tag	wave + sponge absorption zone	wave maker with outgoing absorption over length L	bc_user()
ale(L)#user#tag	active wave generation (ALE), length L	controlled incident wave profile over L	bc_user() (requires ALE=yes)

The outgoing Riemann invariant is preserved for all SSH/depth-type conditions.

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Specifying Values for ssh, h, q

Inline constant — append #value to the BC type:

bc_W = ssh#1.5      ! constant SSH of 1.5 m
bc_E = q#100.0      ! constant discharge of 100 m³/s

User function — append #user and implement bc_user(tag, x, y, b). The global tc (current time in seconds) is available:

MODULE real(rp) FUNCTION bc_user( tag , x , y , b )
   character(len=*), intent(in)           :: tag
   real(rp)        , intent(in), optional :: x , y , b
   select case( tag )
      case('ssh')
         bc_user = 0.5_rp * sin( 2._rp * pi / 44712._rp * tc )  ! M2-like tide
      case default
         call end_program('unknown bc tag: '//tag)
   end select
END FUNCTION bc_user

Time series file — use types q(t), ssh(t), or h(t), and place bc_<name>.txt in bin/:

$ q(t)
0.      100.
3600.   200.
7200.   250.
10800.  300.

First column is time in seconds; second column is the BC value. Linear interpolation is applied.

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Tidal Harmonic BC (tide)

tide.list lists the constituents, one per line after a --- separator:

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M2  255555  28.98410420  0.9081  0.037  349.0  0.000  0.0
S2  273555  30.00000000  0.4227  0.000    0.0  0.000  0.0
K1  165555  15.04106864  0.5305  0.115   45.0 -0.115 -45.0

Columns: name doodson vit_ang(°/h) coef_pot c1 k1 c2 k2

For each constituent <name>, the pair forcing.<name>tide.a / forcing.<name>tide.b must exist in bin/.

At each boundary edge the prescribed SSH is:

A linear ramp (tide_is_ramp, tide_time_ramp) starts the forcing from zero at and is disabled on restart.

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Spatially-Varying SSH Time Series (ssht)

ssht_edge_at_bc.a stores the SSH time series per open boundary edge. ssht_edge_at_bc.b lists the record dates (CNES Julian days). Two records are kept in memory and linearly interpolated in time. Compatible with tide (ssht/tide), in which case contributions are summed.

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Spectral Wave Maker (wave)

The wave BC type prescribes a wave field from a pre-computed spectrum stored in forcing.wave_spectrum.a/.b. The .b file contains the number of boundary edges ne, record dates, the peak frequency f_peak, the number of frequency components f_nb, and the frequency values. The .a binary stores node pairs and complex amplitudes per frequency.

The wave BC is ramped up over nb_period_ramp_wbc wave periods. The flux integration uses nb_pt_sampling_wbc quadrature points per edge.

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Relaxation / Sponge Zones (r, rssh, sshs)

Relaxation zones smoothly transition the solution from the interior state to a prescribed target over a distance L:

• r(L)#user#tag — target value from bc_user(tag), applied as a sponge of length L
• rssh#η#L — target is a constant SSH η, length L inline
• sshs(L)#user#tag — combines wave maker with outgoing absorption; simultaneously generates waves and damps reflections over length L

The relaxation shape is controlled by frelax (default exp6).

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Active Wave Generation (ale)

ale(L)#user#tag uses the ALE (Active Layer Emission) method to generate a prescribed incident wave profile over a zone of length L. Requires compilation with ALE=yes. The wave profile is supplied by bc_user(tag).