/BEM/DAA
Block Format Keyword Doubly Asymptotic Approximation for Underwater Explosion, where the fluid mass matrix is computed by boundary element method.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/BEM/DAA/daa_ID/unit_ID  
daa_title  
surf_ID  grav_ID  
$\rho $  C  P_{min}  
X_{s}  Y_{s}  Z_{s}  
I_{form}  Ipri  Ipres  Kform  Freesurf  Afterflow  Integr 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

P_{m}  $\theta $  a  ${a}_{\theta}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{P}  Fscale_{P} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

X_{c}  Y_{c}  Z_{c} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

X_{A}  Y_{A}  Z_{A}  
DirX  DirY  DirZ 
Definitions
Field  Contents  SI Unit Example 

daa_ID  DAA block
identifier (Integer, maximum 10 digits) 

unit_ID  Unit Identifier (Integer, maximum 10 digits) 

daa_title  DAA block
title (Character, maximum 100 characters) 

surf_ID  Wet surface identifier.
2
3 (Integer) 

grav_ID  /GRAV
option identifier. (Integer) 

$\rho $  Fluid
density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
C  Fluid sound
speed. (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
P_{min}  Pressure cutoff (<
0). Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
X_{s}  Xcoordinate of standoff
point. 3 (Real) 
$\left[\text{m}\right]$ 
Y_{s}  Ycoordinate of standoff
point. 3 (Real) 
$\left[\text{m}\right]$ 
Z_{s}  Zcoordinate of standoff
point. 3 (Real) 
$\left[\text{m}\right]$ 
Iform  BEM solution flag.
(Integer) 

Ipri  Printout flag level.
(Integer) 

Ipres  Pressure loading flag.
6
(Integer) 

Kform  Analysis flag.
(Integer) 

Freesurf  Free surface flag. 6
(Integer) 

Afterflow  Afterflow computation.
7
(Integer) 

Integr  Time integer flag.
(Integer) 

P_{m}  Maximum pressure. 5 (Real) 
$\left[\text{Pa}\right]$ 
$\theta $  Decay
time. (Real) 
$\left[\text{s}\right]$ 
a  Maximum pressure constant.
5 (Real) 

${a}_{\theta}$  Pressure decay time
constant. 5 (Real) 

fct_ID_{P}  Incident pressure function
identifier. (Integer) 

Fscale_{P}  Ordinate (pressure) scale
factor for
fct_ID_{P}. (Real) 
$\left[\text{Pa}\right]$ 
X_{C}  Xcoordinate of explosive
charge. (Real) 
$\left[\text{m}\right]$ 
Y_{C}  Ycoordinate of explosive
charge. (Real) 
$\left[\text{m}\right]$ 
Z_{C}  Zcoordinate of explosive
charge. (Real) 
$\left[\text{m}\right]$ 
X_{A}  Xcoordinate of point A on
the free surface. (Real) 
$\left[\text{m}\right]$ 
Y_{A}  Ycoordinate of point A on
the free surface. (Real) 
$\left[\text{m}\right]$ 
Z_{A}  Zcoordinate of point A on
the free surface. (Real) 
$\left[\text{m}\right]$ 
DirX  Xcomponent of the normal
to the free surface plane. (Real) 

DirY  Ycomponent of the normal
to the free surface plane. (Real) 

DirZ  Zcomponent of the normal
to the free surface plane. (Real) 
Comments
 The entire structure must be modeled. Symmetric analysis is not supported.
 The surface normal $n$ should be pointed into the fluid.
 Standoff point defined with (X_{s}, Y_{s}, Zs) is the location where the incident pressure wave is given at time t=0:
 A plane wave can be simulated using a spherical wave and putting the explosive charge far enough away.
 Pressure at the standoff point as
a function of time is:
(1) $${\mathrm{P}}_{i}\left(t\right)={P}_{m}{e}^{\frac{t}{\theta}}$$Where, ${P}_{m}$
 Maximum pressure
 $t$
 Time
 $\theta $
 Decay time
The maximum pressure and decay time can be calculated using:(2) $${P}_{m}=K{\left[\frac{{W}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.}}{R}\right]}^{a}$$(3) $$\theta ={K}_{\theta}{W}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.}{\left[\frac{{W}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.}}{R}\right]}^{{a}_{\theta}}$$ $W$
 Explosive mass.
 $R$
 Distance to the explosion.
 $K$ , α, ${K}_{\theta}$ and ${a}_{\theta}$
 Constants depending on the explosive.
If $W$ in kg, $R$ in meter, ${P}_{m}$ in MPa and in ms.$K$ α ${K}_{\theta}$ ${a}_{\theta}$ TNT 52.12 1.180 0.0895 0.185 PETN 56.21 1.194 0.0860 0.257 HBX 53.51 1.144 0.0920 0.247  A free surface is a plane defined by a point and its normal vector.
 The afterflow normal velocity is
calculated as:
(4) $${v}_{afterflow}=\frac{\mathrm{cos}\gamma}{\rho R}{\displaystyle {\int}_{0}^{t}P\left(t\right)dt}$$ P
 Fluid point.
 C
 Explosive charge point.
 S
 Standoff point.