Flux specified boundaries

Flux Specified Boundaries Table

ibtype	Location	Normal Flux	Numerical Implementation	Tangential Slip	Typical Use
0	external	zero	essential	free	mainland boundaries
1	internal	zero	essential	free	island boundaries
2	external	nonzero inflow	essential	free	river or ocean inflow boundaries; if flux is periodic it is specified in fort.15; if it is time varying and aperiodic, it must be specified in fort.20 file
3	external	outflow	essential	free	flow over a weir out of the domain; must specify levee height; ADCIRC calculates the fluxes
4	internal	zero or nonzero	essential	free	interior levees; must specify levee height; ADCIRC calculates the fluxes
5	internal	zero or nonzero	essential	free	interior levees with cross-barrier pipes (like a culvert); must specify levee height and other parameters; ADCIRC calculates the fluxes
102	external	nonzero inflow	essential	free	as ibtype 2 but baroclinic instead of barotropic; also requires density-related boundary conditions in fort.39 input file
Boundary types 0-5 and 102 above can introduce instabilities into the ADCIRC solution; types 20-25 and 122 are therefore preferred.
10	external	zero	essential	no slip	as ibtype 0 above but no slip
11	internal	zero	essential	no slip	as ibtype 1 above but no slip
12	external	nonzero	essential	no slip	as ibtype 2 above but no slip
13	external	outflow	essential	no slip	as ibtype 3 above but no slip
112	external	nonzero	essential	no slip	as ibtype 12 but baroclinic instead of barotropic; also requires density-related boundary conditions in fort.39 input file
Avoid boundary types 10-13 and 112 unless very high mesh resolution is provided to allow resolution of the lateral boundary layer.
20	external	zero (weak)	natural	free	as ibtype 0 but natural boundary; preferred over ibtype 0 or 10. ADCIRC satisfies this by default.
21	internal	zero (weak)	natural	free	as ibtype 1 but natural boundary; preferred over ibtype 1 or 11. ADCIRC satisfies this by default.
22	external	nonzero (weak)	natural	free	as ibtype 2 but natural boundary; preferred over ibtype 2 or 12
23	external	outflow (weak)	natural	free	as ibtype 3 but natural boundary; preferred over ibtype 3 or 13
24	internal	zero or nonzero (weak)	natural	free	as ibtype 4 but natural boundary; preferred over ibtype 4
25	internal	zero or nonzero (weak)	natural	free	as ibtype 5 but natural boundary; preferred over ibtype 5
122	external	nonzero (weak)	natural	free	as ibtype 22 but baroclinic instead of barotropic; also requires density-related boundary conditions in fort.39 input file
Boundary types 20-25 and 122 are preferred over the corresponding essential boundary conditions (types 0-5 and 102).

Essential boundaries with free slip are applied by specifying the contribution (zero or non-zero) to the normal boundary flux integral in the continuity equation and by specifying the (zero or non-zero) normal velocity in the momentum equations. This boundary condition should satisfy the flux balance in a global sense and the normal flux at each boundary node.

Essential boundaries with no slip are applied by specifying the contribution (zero or non-zero) to the normal boundary flux integral in the continuity equation and by setting the (zero or non-zero) normal velocity and zero tangential velocity rather than solving momentum equations along the boundary. This boundary condition should correctly satisfy the normal flux balance in a global sense and zero tangential velocity at each boundary node.

Natural boundaries are applied by specifying the zero or non-zero contribution to the normal boundary flux integral in the continuity equation. There is no constraint on velocity (normal or tangential) in the momentum equations. This boundary condition should correctly satisfy the flux balance in a global sense but will only satisfy the normal flow at each boundary node in the limit of infinite resolution.

General Notes for Normal Flow Boundary Conditions

All external (external no normal flow, external with specified normal flow and external barrier) boundaries should be listed in consecutive order around the outside of the entire domain before any internal (island with no normal flow or internal barrier) boundary segments are listed. Internal barrier boundaries that intersect an external boundary should be specified separately, even though this will result in some nodes being specified in both boundaries, (see below).

An external no normal flow or specified normal flow boundary that completely surrounds the domain (e.g., a lake) should be closed by repeating the first node as the last node.

All no normal flow internal boundaries (e.g., islands) should be closed by repeating the first node as the last node.

Unless the boundary segment is closed, always start listing the boundary nodes where two boundaries connect.

When an external specified normal flow or external barrier boundary connects to an external no normal flow boundary, the initial leg of the external specified normal flow boundary or external barrier boundary is used to determine the normal and tangential direction at the node common to both boundaries.

External boundaries with specified (non-zero) normal flow boundary conditions and external barrier boundaries can not connect. They must be separated by an external no normal flow boundary or an elevation specified boundary.

An internal barrier boundary can intersect an external no normal flow boundary. (For example a levee may project out of an external no normal flow boundary in which case 2 nodes, the front and back node on the internal barrier boundary, would be common to the external boundary.) However, the common external nodes must be treated in the weak sense. ADCIRC will automatically accommodate this as follows:

• If the external no flow boundary is specified as essential with slip (IBTYPE(k)=0) and the internal barrier boundary is specified as essential with slip (IBTYPE(k)=4), the common external boundary nodes are automatically changed to natural no flow boundary nodes (IBTYPE(k)=20).
• If the external no flow boundary is specified as essential with no slip (IBTYPE(k)=10) and the internal barrier boundary is specified as essential with slip (IBTYPE(k)=4), the common external boundary nodes are automatically changed to natural no flow boundary nodes (IBTYPE(k)=20).
• If the external no flow boundary is specified as natural with slip (IBTYPE(k)=20) and the internal barrier boundary is specified as essential with slip (IBTYPE(k)=4), no changes are made.
• If the external no flow boundary is specified as essential with slip (IBTYPE(k)=0) and the internal barrier boundary is specified as natural with slip (IBTYPE(k)=24), no changes are made.
• If the external no flow boundary is specified as essential with no slip (IBTYPE(k)=10) and the internal barrier boundary is specified as natural with slip (IBTYPE(k)=24), the common external boundary nodes are automatically changed to essential no flow with slip boundary nodes (IBTYPE(k)=0).
• If the external no flow boundary is specified as natural with slip (IBTYPE(k)=20) and the internal barrier boundary is specified as natural with slip (IBTYPE(k)=24), no changes are made.

Internal barrier boundaries can not intersect external specified flow boundary segments, external barrier boundary segments or internal no normal flow boundaries.

For all normal flow boundaries (i.e. IBTYPE(k) = 0,1,2,3, 4,10,11,12,13,20,21,22,23,24,30), the boundary flux integral in the continuity equation is evaluated with the appropriate (zero, specified or computed) flux. This is a natural boundary condition. For natural normal flow boundaries (IBTYPE(k) = 20,21,22,23,24), this is the only lateral boundary condition that is used.

For essential normal flow boundaries with tangential slip (IBTYPE(k) = 0,1,2,3,4,10,11,12,13), the normal direction momentum equation (obtained by re-orienting the x/y momentum equations into normal/tangential directions) is eliminated and the normal velocity is set by dividing the normal flux per unit width (zero, specified, or computed) by the total water column height.

For essential normal flow boundaries with no tangential slip (IBTYPE(k) = 10,11, 12,13), both momentum equations are eliminated. The tangential velocity is set equal to zero and the normal velocity is set by dividing the normal flux per unit width (zero, specified, or computed) by the total water column height. Use of this boundary condition requires considerable care since strictly speaking this type of no slip boundary condition is only mathematically justifiable if lateral viscous terms are used in the simulation and only physically justifiable if the lateral boundary layers are sufficiently resolved.

External Barrier Boundary Note

(IBTYPE(k) = 3, 13, 23)

Outward flow per unit width, QN2(k,j), normal to and over an external barrier boundary is computed as:

Case 1 water level below or equal to the barrier height

QN2(k,j) = 0

Case 2 water level above the barrier height

QN2(k,j) = -(2/3)*BARLANCFSP(k,j)*RBARWL*((2/3)*RBARWL*G)**0.5

where, RBARWL = ETA1(NBVV(k,j))-BARLANHT(k,j) = water height above the barrier

ETA1(NBVV(k,j)) = water level computed at the previous time step at node NBVV(k,j)

This formula is given by Leendertse (Aspects of SIMSYS2D ? A System for Two-Dimensional Flow Computation, Rand/R-3572-USGS, 1987) and is simply the formula for a broad crested weir (e.g., see Henderson, Open Channel Flow, section 6.6).

See also General Notes for Normal Flow Boundary Conditions

Internal Barrier Boundary Note

(IBTYPE(k) = 4, 24)

An internal barrier boundary consists of a long thin island with parallel front and back faces. Pairs of nodes are placed on either side of the boundary so as to provide a one to one correspondence between the nodes on the front face and back faces. Flow is assumed to go across the boundary from one node to its paired node on the opposite side. The normal flow is equal in magnitude and opposite in sign on the two sides of the boundary (e.g., outflow on the front face = inflow on the back face). Normal flow per unit width, QN2(k,j), at internal barrier boundary node NBVV(k,j) and its paired node IBCONN(k,j) is computed as:

Case 1 water level below or equal to the barrier height on both sides of the barrier

QN2(k,j) = 0

Case 2 water level above the barrier height but equal on both sides of the barrier

QN2(k,j) = 0

Case 3 water level above the barrier height but greater on the front side than on the back with subcritical flow across the barrier. Subcritical flow from front to back across the barrier occurs if the water level height above the barrier on the back side is greater than 2/3 the water level height above the barrier on the front side (i.e., RBARWL2 > 0.667*RBARWL1).

QN2(k,j) = -RAMP*BARINCFSB(k,j)*RBARWL2*(2*G*(RBARWL1-RBARWL2))**0.5

Case 4 water level above the barrier height but greater on the front side than on the back with supercritical flow across the barrier. Supercritical flow from front to back across the barrier occurs if the water level height above the barrier on the back side is less than or equal to 2/3 the water level height above the barrier on the front side (i.e., RBARWL2 < 0.667*RBARWL1).

QN2(k,j) = -(2/3)*RAMP*BARINCFSP(k,j)*RBARWL1*((2/3)*RBARWL1*G)**0.5

Case 5 water level above the barrier height but greater on the back side than on the front with subcritical flow across the barrier. Subcritical flow from back to front across the barrier occurs if the water level height above the barrier on the front side is greater than 2/3 the water level height above the barrier on the back side (i.e., RBARWL1 > 0.667*RBARWL2).

QN2(k,j) = RAMP*BARINCFSB(k,j)*RBARWL1*(2*G*(RBARWL2-RBARWL1))**0.5

Case 6 water level above the barrier height but greater on the back side than on the front with supercritical flow across the barrier. Supercritical flow from back to front across the barrier occurs if the water level height above the barrier on the front side is less than or equal to 2/3 the water level height above the barrier on the back side (i.e., RBARWL1 < 0.667*RBARWL2).

QN2(k,j) = (2/3)*RAMP*BARINCFSP(k,j)*RBARWL2*((2/3)*RBARWL2*G)**0.5

where

RBARWL1 = ETA1(NBVV(k,j))-BARINHT(k,j) = water height above the barrier on the front side of the barrier

RBARWL2 = ETA1(IBCONN(k,j))- BARINHT(k,j) = water height above the barrier on the back side of the barrier

ETA1(NBVV(k,j)) = water level computed at the previous time step on the front side of the barrier

ETA1(IBCONN(k,j)) = water level computed at the previous time step on the back side of the barrier

These formulae are given by Leendertse (Aspects of SIMSYS2D ? A System for Two-Dimensional Flow Computation, Rand/R-3572-USGS, 1987) and are simply the formulae for a broad crested weir (e.g., see Henderson, Open Channel Flow, section 6.6).

See also General Notes for Normal Flow Boundary Conditions

Internal Barrier Boundary with Cross Barrier Pipes Note

(IBTYPE(k) = 5,25)

This type differs from IBTYPE(k)=5 or 25 This type differs from IBTYPE(k)=4 and 24 in that the barrier contains a cross barrier pipe with a specified height, pipe coefficient, and pipe diameter. The formulation of this boundary type is described in detail in the Technical Publication “Leaky Internal-Barrier Normal-Flow Boundaries in the ADCIRC Coastal Hydrodynamics Code“.

Because this boundary type has so much in common with IBTYPE(k)=4 or 24, only the differences will be described here. Normal flow per unit width, QN2(k,j), at internal barrier boundary with cross barrier pipes node NBVV(k,j) and its paired node IBCONN(k,j) is computed as:

Case 1: Water level on both sides of the internal barrier below the height of the crown of the cross barrier pipe

QN2(k,j) = 0

Case 2: Water level on both sides of the internal barrier equal

QN2(k,j) = 0

Case 3: Water elevation on the front side of the internal barrier greater than water elevation on the back side; water elevation on the front side greater than the crown height of the cross-barrier pipe; and water elevation on the back side below crown height of the pipe

QN2(k,j) = -RAMP*(0.25*pi*D^2)*(2*G*RBARWL1/(1+PIPECOEFR(k,j)))^0.5

where

RBARWL1 = ETA2(NBVV(k,j))-PIPEHTR(k,j)

Case 4: Water elevation on the front side of the internal barrier greater than water elevation on the back side; water elevation on the front side greater than the crown height of the cross barrier pipe; and water elevation on the back side above the crown height of the pipe.

QN2(k,j) = -RAMP*0.25*pi*PIPEDIAMR^2*(2*G*(RBARWL1-RBARWL2)/PIPECOEF(k,j))^0.5

where

RBARWL1 = ETA2(NBVV(k,j))-PIPEHTR(k,j)

RBARWL2 = ETA2(IBCONN(k,j))-PIPEHTR(k,j)

Case 5: Water elevation on the back side of the internal barrier greater than water elevation on the front side; water elevation on the back side greater than the crown height of the cross-barrier pipe; and water elevation on the front side below the crown height of the pipe.

QN2(I)= RAMP*0.25*pi*(PIPEDIAMR)^2 * (2*G*RBARWL2 / (1 +/PIPECOEF(k,j)))^0.5

where

RBARWL2 = ETA2(IBCONN(k,j))-PIPEHTR(k,j)

Case 6: Water elevation on the back side of the internal barrier greater than water elevation on the front side; water elevation on the back side greater than the crown height of the cross-barrier pipe; and water elevation on the front side above the crown height of the pipe.

QN2(I)= RAMP**0.25*pi*(PIPEDIAMR(k,j))^2*(2*G*(RBARWL2-RBARWL1)/PIPECOEFR(k,j))^0.5

where

RBARWL1 = ETA2(NBVV(k,j))-PIPEHTR(k,j)

RBARWL2 = ETA2(IBCONN(k,j))-PIPEHTR(k,j)

Details of the rationale and implementation of this boundary type can be found in the following reference:

Westerink, J.J., R.A. Luettich and A. Militello, 2001, Leaky internal-barrier normal-flow boundaries in the ADCIRC coastal hydrodynamics code, Coastal and Hydraulic Engineering Technical Note ERDC/CHL CHETN-IV-32, U.S. Army Engineer Research and Development Center, Vicksburg, MS., February 2001, 28p.