GfsVariableStreamFunction

From Gerris

GfsVariableStreamFunction is used to maintain a consistent (i.e. discretely non-divergent) velocity field defined by its streamfunction. Both the cell-centered and face-centered (i.e. MAC) velocity fields are maintained.

Note that this object can only be used for 2D simulations.

The syntax in parameter files is

[ GfsVariableFunction ]

Examples

• Convergence of the Godunov advection scheme

  VariableStreamFunction Psi -4.*(x*x + y*y)

• Time-reversed VOF advection in a shear flow

    VariableStreamFunction {
	# make sure that the entire field is reinitialised at t = 2.5
	step = 2.5 
    } Psi (t < 2.5 ? 1. : -1.)*sin((x + 0.5)*M_PI)*sin((y + 0.5)*M_PI)/M_PI

• Time-reversed advection of a VOF concentration

    VariableStreamFunction {
	step = 2.5 
    } Psi (t < 2.5 ? 1. : -1.)*sin((x + 0.5)*M_PI)*sin((y + 0.5)*M_PI)/M_PI

• Time-reversed advection with curvature-based refinement

    VariableStreamFunction {
	# make sure that the entire field is reinitialised at t = 2.5
	step = 2.5 
    } Psi (t < 2.5 ? 1. : -1.)*sin((x + 0.5)*M_PI)*sin((y + 0.5)*M_PI)/M_PI

• Numerical viscosity for vorticity/streamfunction formulation

  VariableStreamFunction { istep = 1 } Psi1 Psi

• Advection of a cosine bell around the sphere

  VariableStreamFunction Psi -U0*(sin (y*DTR)*cos (DTR*ALPHA) - cos (x*DTR)*cos (y*DTR)*sin (DTR*ALPHA))