# GfsBoundary

Revision as of 06:17, 16 April 2009; view current revision

### Examples

• B\'enard--von K\'arm\'an Vortex Street for flow around a cylinder at Re=160
• ```  left = Boundary {
BcDirichlet U 1
BcDirichlet T { return y < 0. ? 1. : 0.; }
}
```

• Vortex street around a "heated" cylinder
• ```  left = Boundary {
BcDirichlet U 1
}
```

• Parallel simulation on four processors
• ```  left = Boundary {
BcDirichlet U 1
BcDirichlet T { return y < 0. ? 1. : 0.; }
}
```

• Collapse of a column of grains
• ```    top = Boundary {
# shift the reference pressure by the hydrostatic pressure of
# the light phase, i.e. P = 0 at the bottom boundary in the
# light phase. I am not sure whether this makes a real
# difference.
BcDirichlet P -RHOF*LDOMAIN
BcNeumann V 0
}
```

```    bottom = Boundary {
# no-slip at the bottom
BcDirichlet U 0
}
```

```    right = Boundary {
BcDirichlet V 0
}
```

• Viscous folding of a fluid interface
• ```    bottom = Boundary {
BcDirichlet U 0
}
```

```    left = Boundary {
BcDirichlet V 0
}
```

```    right = Boundary {
BcDirichlet V 0
}
```

```    left = Boundary {
BcDirichlet U velocity_bc(y, t)
}
```

```    bottom = Boundary {
BcDirichlet U 0
}
```

```    bottom = Boundary {
BcDirichlet U 0
}
```

• Turbulent air flow around RV Tangaroa
• ```    left = Boundary {
BcDirichlet U 1
}
```

```    right = Boundary {
BcNeumann U 0
BcDirichlet P 0
}
```

• Atomisation of a pulsed liquid jet
• ```    left = Boundary {
# Pulsed jet on inflow
BcDirichlet U T0*(1. + 0.05*sin (10.*2.*M_PI*t))
BcDirichlet T T0
BcDirichlet V 0
BcDirichlet W 0
}
```

• Air-water flow around a Series 60 cargo ship
• ```    left = Boundary {
BcDirichlet P 0
BcDirichlet V 0
BcDirichlet W 0
BcNeumann U 0
BcNeumann T 0
}
```

```    right = Boundary {
BcDirichlet P 0
BcDirichlet V 0
BcDirichlet W 0
BcNeumann U 0
BcNeumann T 0
}
```

• Lunar tides in Cook Strait, New Zealand
• ```    left = Boundary {
BcFlather U 0 H P M2(t)
}
```

```    right = Boundary {
BcFlather U 0 H P M2(t)
}
```

```    top = Boundary {
BcFlather V 0 H P M2(t)
}
```

```    bottom = Boundary {
BcFlather V 0 H P M2(t)
}
```

• Small amplitude solitary wave interacting with a parabolic hump
• ```    left = Boundary { BcNeumann U 0 }
```

```    top = Boundary { BcNeumann V 0 }
```

```    bottom = Boundary { BcNeumann V 0 }
```

```    right = Boundary { BcNeumann U 0 }
```

```    top = Boundary { BcNeumann V 0 }
```

```    bottom = Boundary { BcNeumann V 0 }
```

• Shock reflection by a circular cylinder
• ```    left = Boundary {
BcDirichlet P 3.505271526
BcDirichlet U 22.049341608
}
```

```    top = Boundary
```

• Tsunami runup onto a complex three-dimensional beach
• ```    left = Boundary { BcSubcritical U (input - Zb) }
```

• The 2004 Indian Ocean tsunami
• ```    top = Boundary {
BcSubcritical V -Zb
}
```

```    bottom = Boundary {
BcSubcritical V -Zb
}
```

```    right = Boundary {
BcSubcritical U -Zb
}
```

```    left = Boundary {
BcSubcritical U -Zb
}
```

• Convergence of the Poisson solver
• ```  left =   Boundary { BcDirichlet P (sin (M_PI*3.*x)*sin (M_PI*3.*y)) }
```

```  right =  Boundary { BcDirichlet P (sin (M_PI*3.*x)*sin (M_PI*3.*y)) }
```

```  top =    Boundary { BcDirichlet P (sin (M_PI*3.*x)*sin (M_PI*3.*y)) }
```

```  bottom = Boundary { BcDirichlet P (sin (M_PI*3.*x)*sin (M_PI*3.*y)) }
```

• Convergence with a refined circle
• ```   left =   Boundary { BcNeumann P (- 3.*M_PI*cos(M_PI*3.*x)*sin (M_PI*3.*y)) }
```

```   right =  Boundary { BcNeumann P (  3.*M_PI*cos(M_PI*3.*x)*sin (M_PI*3.*y)) }
```

```   top =    Boundary { BcNeumann P (  3.*M_PI*cos(M_PI*3.*y)*sin (M_PI*3.*x)) }
```

```   bottom = Boundary { BcNeumann P (- 3.*M_PI*cos(M_PI*3.*y)*sin (M_PI*3.*x)) }
```

• Rotation of a straight interface
• ```    left = Boundary {
BcDirichlet U y
BcAngle T (90. + atan2(1.,t)*180./M_PI)
}
```

```    right = Boundary {
BcDirichlet U y
BcAngle T (90. - atan2(1.,t)*180./M_PI)
}
```

```    top = Boundary {
BcDirichlet U y
BcAngle T (180. - atan2(1.,t)*180./M_PI)
}
```

```    bottom = Boundary {
BcDirichlet U y
BcAngle T atan2(1.,t)*180./M_PI
}
```

• Potential flow around a sphere
• ```    left = Boundary { BcDirichlet U U0 }
```

```    right = Boundary { BcDirichlet U U0 }
```

• Viscous flow past a sphere
• ```    left = Boundary { BcDirichlet U U0 }
```

• Mass conservation
• ```    left = Boundary {
BcDirichlet U 1
BcDirichlet V 0
}
```

• Mass conservation with solid boundary
• ```    left = Boundary {
BcDirichlet U 1
BcDirichlet V 0
}
```

• Boundary layer on a rotating disk
• ```    left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
BcDirichlet W y
}
```

```    right = Boundary {
BcNeumann U 0
BcNeumann V 0
BcNeumann W 0
BcDirichlet P 0.
}
```

```    bottom = Boundary { BcDirichlet W 0 }
```

```    left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
BcDirichlet W y
}
```

```    right = Boundary {
BcNeumann U 0
BcNeumann V 0
BcNeumann W 0
BcDirichlet P 0.
}
```

```    left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
BcDirichlet W y
}
```

```    right = Boundary {
BcNeumann U 0
BcNeumann V 0
BcNeumann W 0
BcDirichlet P 0.
}
```

```    left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
BcDirichlet W y
}
```

```    right = Boundary {
BcNeumann U 0
BcNeumann V 0
BcNeumann W 0
BcDirichlet P 0.
}
```

```    top = Boundary {
BcNeumann U 0
BcNeumann V 0
BcNeumann W 0
}
```

• Lid-driven cavity at Re=1000
• ```  top = Boundary {
BcDirichlet U 1
BcDirichlet V 0
}
```

```  bottom = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  right = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

• Lid-driven cavity at Re=1000 (explicit scheme)
• ```  top = Boundary {
BcDirichlet U 1
BcDirichlet V 0
}
```

```  bottom = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  right = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

• Lid-driven cavity with a non-uniform metric
• ```  top = Boundary {
BcDirichlet U 1
BcDirichlet V 0
}
```

```  bottom = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  right = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

• Lid-driven cavity on an anisotropic mesh
• ```  top = Boundary {
BcDirichlet U 1
BcDirichlet V 0
}
```

```  right = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  bottom = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  right = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

```  left = Boundary {
BcDirichlet U 0
BcDirichlet V 0
}
```

• Poiseuille flow
• ```    bottom = Boundary {
BcDirichlet U 0
}
```

```    top = Boundary {
BcDirichlet U 0
}
```

• Bagnold flow of a granular material
• ```    top = Boundary {
BcNeumann V 0
BcDirichlet P 0
}
```

```    bottom = Boundary {
BcDirichlet U 0
}
```

• Poiseuille flow with metric
• ```    bottom = Boundary {
BcDirichlet U 0
}
```

```    top = Boundary {
BcDirichlet U 0
}
```

• Wind-driven lake
• ```    top = Boundary {
BcNeumann U 1.
}
```

```    bottom = Boundary {
BcDirichlet U 0
}
```

• Convergence of a potential flow solution
• ```    left = Boundary { BcDirichlet U 1 }
```

```    right = Boundary { BcDirichlet U 1 }
```

• Flow through a divergent channel
• ```GfsBox { left = Boundary { BcDirichlet U 1 } }
```

• Potential flow around a thin plate
• ```  left = Boundary { BcDirichlet U 1 }
```

• Translation of an hexagon in a uniform flow
• ```    left = Boundary {
BcDirichlet U 1
BcDirichlet T 1
}
```

• Sessile drop
• ```    bottom = Boundary {
BcAngle T ANGLE
}
```

```    left = Boundary # axis of symmetry
```

• Transcritical flow over a bump
• ```    right = Boundary {
BcDirichlet P 0.33
BcNeumann U 0
}
```

```    left = Boundary {
BcDirichlet U 0.18
}
```

• Transcritical flow with multiple layers
• ```    right = Boundary {
# set water depth at outlet
BcDirichlet P HE
BcNeumann U 0
}
```

```    left = Boundary {
# set flow rate at inlet, evenly distributed over all layers
BcDirichlet U Q/NL
}
```

• Circular dam break on a sphere
• ```    right = Boundary { BcNeumann U 0 }
```

```    left = Boundary { BcNeumann U 0 }
```

```    top = Boundary { BcNeumann V 0 }
```

```    bottom = Boundary { BcNeumann V 0 }
```

• Circular dam break on a rotating sphere
• ```    right = Boundary { BcNeumann U 0 }
```

```    left = Boundary { BcNeumann U 0 }
```

```    top = Boundary { BcNeumann V 0 }
```

```    bottom = Boundary { BcNeumann V 0 }
```

• Creeping Couette flow between cylinders
• ```    left  = Boundary {
BcDirichlet V 0.25
BcDirichlet T 0.25
}
```

```    right = Boundary {
BcDirichlet V 0.
BcDirichlet T 0
}
```

• Flow between eccentric cylinders using bipolar coordinates
• ```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

```    left = Boundary { BcDirichlet V 0 }
```

```    right = Boundary { BcDirichlet V 1 }
```

• Dielectric-dieletric planar balance
• ```   top   = Boundary {
BcDirichlet Phi  1
BcDirichlet P 0
}
```

```   bottom = Boundary {
BcDirichlet Phi 0.
}
```

• Balance with solid boundaries
• ```    top   = Boundary {
BcDirichlet Phi  1
BcDirichlet P 0
}
```

```    bottom = Boundary {
BcDirichlet Phi 0.
}
```

• Relaxation of a charge bump
• ```    left   = Boundary { BcDirichlet Phi 0 }
```

```    right  = Boundary { BcDirichlet Phi 0 }
```

```    top    = Boundary { BcDirichlet Phi 0 }
```

```    bottom = Boundary { BcDirichlet Phi 0 }
```

• Charge relaxation in an axisymmetric insulated conducting column
• ```    top = Boundary { BcDirichlet Phi 0 }
```

• Charge relaxation in a planar cross-section
• ```    top = Boundary { BcDirichlet Phi 0 }
```

```    bottom = Boundary { BcDirichlet Phi 0 }
```

```    left = Boundary { BcDirichlet Phi 0 }
```

```    right = Boundary { BcDirichlet Phi 0 }
```

• Equilibrium of a droplet suspended in an electric field
• ```    right = Boundary {
BcDirichlet Phi Ef*x
}
```

```    left = Boundary {
BcDirichlet Phi Ef*x
}
```

```    top = Boundary {
BcDirichlet Phi Ef*x
}
```

• Gouy-Chapman Debye layer
• ```    top = Boundary
```

```    left = Boundary {
BcDirichlet Phi Volt
BcDirichlet Cpos exp(-Volt)
BcDirichlet Cneg exp(Volt)
}
```

```    top = Boundary
```

```    top = Boundary
```

```    top = Boundary
```

```    top = Boundary
```

```    right = Boundary {
BcDirichlet Phi 0.
BcDirichlet Cpos 1.
BcDirichlet Cneg 1.
}
```

• Simple example of groundwater flow following Darcy's law
• ```    top = Boundary {
BcDirichlet P 0
BcDirichlet U 0
BcNeumann V 0
}
```

```    left = Boundary {
BcDirichlet P -M_PI/2
BcNeumann U 0
BcDirichlet V 0
}
```

• Groundwater flow with piecewise constant permeability
• ```    top = Boundary {
BcDirichlet P 0
BcDirichlet U 0
BcNeumann V 0
}
```

```    left = Boundary {
BcDirichlet P -2*M_PI/3
BcNeumann U 0
BcDirichlet V 0
}
```