/BEM/FLOW

Block Format Keyword Describes the incompressible fluid flow by boundary elements method.

Format

(1)	(2)	(3)	(4)	(5)	(7)
/BEM/FLOW/`flow_ID`/`unit_ID`
`flow_title`
`surf_ID`_ex	`N`_io	`I`_inside	`fct_ID`_fsp	`Fscale`_fsp	`Ascale`_fsp
`grn_ID`_aux	`I`_test	`Tole`
`Rho`		`I`_vinf

If N_io > 0, insert N_io times line

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`surf_ID`_io	`fct_ID`_nv	`fct_ID`_p		`Fscale`_nv		`Fscale`_p		`Ascale`_t

Formulation flag

(1)	(2)	(3)	(4)	(5)
`I`_form	`I`_pri	`Dt`_flow
`fct_ID`_v	`Fscale`_v		`Ascale`_v
`Dir`_x		`Dir`_y		`Dir`_z

Definitions

Field	Contents	SI Unit Example
`flow_ID`	Incompressible flow block identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`flow_title`	Incompressible flow block title. (Character, maximum 100 characters)
`surf_ID`_ex	Flow external surface identifier. (Integer)
`N`_io	Number of inflow-outflow surfaces. (Integer)
`I`_inside	Inside or outside flow flag. = 1 (Default) Flow is computed inside the surface defined by `surf_ID`_ex. The surface element normals must be oriented outwards. = 2 Flow is computed outside the surface defined by `surf_ID`_ex. The surface element normals must be oriented inwards. (Integer)
`fct_ID`_fsp	Stagnation pressure curve identifier. (Integer)
`Fscale`_fsp	Stagnation pressure scale factor. Default = 1.0 (Real)	$[Pa]$
`Ascale`_fsp	Abcissa scale factor for stagnation pressure curve. Default = 1.0 (Real)	$[s]$
`grn_ID`_aux	Auxiliary nodes group identifier. 2 (Integer)
`I`_test	Test auxiliary nodes flag. 2 (Integer > 0)
`Tole`	A dimensional tolerance. 2 Default = 1.e-5 (Real)
`Rho`	Fluid density. (Real)	$[\frac{kg}{m^{3}}]$
`I`_vinf	Additional velocity field flag. 3 (Integer > 0)
`surf_ID`_io	Inflow-Outflow surface identifier. 4 (Integer)
`fct_ID`_nv	Normal velocity curve. 4 (Integer)
`fct_ID`_p	Imposed pressure curve. 5 (Integer)
`Fscale`_nv	Normal velocity scale factor. Default = 1.0 (Real)	$[\frac{m}{s}]$
`Fscale`_p	Imposed pressure scale factor. Default = 1.0 (Real)	$[Pa]$
`Ascale`_t	Abscissa scale factor for normal velocity curve and imposed pressure curve. Default = 1.0 (Real)	$[s]$
`I`_form	Formulation flag. 6 = 1 (Default) Fluid flow is computed using BEM with a collocation approach to solve the integral equation. = 2 Fluid flow is computed using BEM with a Galerkin approach to solve the integral equation. (Integer > 1)
`I`_pri	Output level. (Integer > 1)
`Dt`_flow	Time step for BEM matrices assembly. 7 = 0 (Default) $Δ t$ used to update to BEM matrices. ≠ 0 $\max (D t_{f l o w}, Δ t)$ used to update to BEM matrices. (Real)	$[s]$
`fct_ID`_v	Velocity curve identifier. (Integer)
`Fscale`_v	Velocity scale factor. Default = 1.0 (Real)	$[\frac{m}{s}]$
`Ascale`_v	Abscissa scale factor for velocity curve. Default = 1.0 (Real)	$[s]$
`Dir`_x	X component of the additional field direction vector. (Real)
`Dir`_y	Y component of the additional field direction vector. (Real)
`Dir`_z	Z component of the additional field direction vector. (Real)

Example

In this example, set normal velocity on surface surf_ID_io=2 and pressure on surface surf_ID_io=1. Auxiliary nodes are inside of closed surface surf_ID_ex=3.

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/BEM/FLOW/1
Flow 1
#surf_IDex       Nio   Iinside fct_IDfsp          Fscale_fsp          Ascale_fsp
         3         2         1         0                  0.                  0.
#grn_IDaux     Itest                Tole
         1         0                1e-5
#                Rho     Ivinf
                 1.0         0
#surf_IDio  fct_IDnv   fct_IDp                     Fscale_nv            Fscale_p            Ascale_t
         2         1         0                          10.0                 0.0                 1.0
#surf_IDio  fct_IDnv   fct_IDp                     Fscale_nv            Fscale_p            Ascale_t
         1         0         1                           0.0            101325.0                 1.0
#    Iform      Ipri             Dt_flow
         1         1                1e-3
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
Function 1
#                  X                   Y
                   0                   1                                                            
                 100                   1                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

The surf_ID_ex must define a closed surface.
Using BEM, the flow potential, velocity and pressure are computed for nodes belonging to the surface defined by surf_ID_ex.
For visual and post-treatment concerns, the flow characteristics can be computed for a set of nodes inside the flow belonging to grn_ID_aux.

If I_test = 1, whether the auxiliary nodes are actually located inside (if I_inside =1) or outside (if I_inside =2), the surface defined by surf_ID_ex at each time step is tested. Inorrect nodes are then canceled for the current time step.

Tolerance Tole is used to perform the point-inside-closed-surface test.
Flag I_vinf is only effective for flow computation in an unbounded domain outside the surface defined by surf_ID_ex (I_inside =2).
If I_vinf = 1, an inflow condition is defined by an additional homogeneous flow defined in free space. The computed flow will be identical to the additional flow at an infinite distance from the surface defined by surf_ID_ex.
If I_inside = 0: Flow is computed inside the surface defined by surf_ID_ex. There must be at least one surface where the normal velocity is imposed and only one surface where the normal velocity could be left as free. The velocity at the free surface will be computed thanks to flux equilibrium on the global surface defined by surf_ID_ex.
If I_inside = 2 and I_vinf = 0: I_inside = 0 but flow is computed outside the surface defined by surf_ID_ex.

If I_inside = 2 and I_vinf = 1: numbers of surface could be free and the normal velocity must be imposed on all of them.
In order to reduce pressure from the velocity field, one and only one pressure must be imposed for the entire flow computation: it can be either the global stagnation pressure or the pressure at one of the inflow-outflow surfaces.
The collocation approach is faster but may not be robust enough to handle very complex geometries.
The Galerkin approach works in every situation but is significantly slower.
BEM matrices depend only on the geometry of the surface.
If Dt_flow = 0 (default), they are assembled at every cycle of the simulation (the time step being classically given by the stability condition of finite elements).

If Dt_flow ≠ 0: max(Dt_flow, Dt) is used to update to BEM matrices; where Dt is the finite element time step.