GfsBcNeumann

From Gerris

GfsBcNeumann is used to impose a Neumann boundary condition i.e. the value of the derivative normal to the boundary of a given variable. The normal vector always points toward the outside of the simulation domain.

The syntax in parameter files is

[ GfsBc ] [ GfsFunction ]

where the GfsFunction is the value of the normal derivative.

Examples

• Collapse of a column of grains

	BcNeumann V 0

• Turbulent air flow around RV Tangaroa

	BcNeumann U 0

• Air-water flow around a Series 60 cargo ship

        BcNeumann U 0

        BcNeumann T 0

        BcNeumann U 0

        BcNeumann T 0

• 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 }

• 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)) }

• Boundary layer on a rotating disk

	BcNeumann U 0

	BcNeumann V 0

	BcNeumann V 0

	BcNeumann W 0

	BcNeumann U 0

	BcNeumann V 0

	BcNeumann W 0

	BcNeumann W 0

	BcNeumann U 0

	BcNeumann V 0

	BcNeumann W 0

	BcNeumann U 0

	BcNeumann V 0

	BcNeumann W 0

	BcNeumann U 0

• Bagnold flow of a granular material

        BcNeumann V 0

• Wind-driven lake

	BcNeumann U 1.

• Transcritical flow over a bump

	BcNeumann U 0

• Transcritical flow with multiple layers

	BcNeumann U 0

• 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 }

• Simple example of groundwater flow following Darcy's law

	BcNeumann V 0

	BcNeumann U 0

• Groundwater flow with piecewise constant permeability

	BcNeumann V 0

	BcNeumann U 0