GfsAdvection

From Gerris

Examples

• Convergence of the Godunov advection scheme

1 0 GfsAdvection GfsBox GfsGEdge {} {
  Time { end = 0.785398 }
  Refine LEVEL
  VariableTracer {} T { gradient = gfs_center_gradient }
  AdvectionParams { cfl = 0.5 }
  Init {} {
    U = -8.*y
    V = 8.*x
    T = {
      double r2 = x*x + y*y; 
      double coeff = 20. + 20000.*r2*r2*r2*r2;
      return (1. + cos(20.*x)*cos(20.*y))*exp(-coeff*r2)/2.;
    }
  }
  OutputErrorNorm { start = end } { awk '{ print LEVEL " " $5 " " $7 " " $9}' } { v = T } {
    s = {
      double r2 = x*x + y*y; 
      double coeff = 20. + 20000.*r2*r2*r2*r2;
      return (1. + cos(20.*x)*cos(20.*y))*exp(-coeff*r2)/2.;
    }
  }
}

• Time-reversed VOF advection in a shear flow

1 0 GfsAdvection GfsBox GfsGEdge {} {
    Time { end = 5 }
    Refine 8

    # Add tracer T, using a VOF advection scheme.
    # The default scheme is a Van-Leer limited, second-order upwind scheme.
    VariableTracerVOF T

    InitFraction T (ellipse (0, -.236338, 0.2, 0.2))

    # Initialize U and V with the vortical shear flow field
    Init {} {
        U = sin((x + 0.5)*M_PI)*cos((y + 0.5)*M_PI)
        V = -cos((x + 0.5)*M_PI)*sin((y + 0.5)*M_PI)
    }

    # At t = 2.5 re-initialize U and V with the reversed flow field
    Init { start = 2.5 } { U = -U V = -V }
    
    # Adapt the mesh dynamically so that at any time the maximum of the gradient
    # of T is less than 1e-2 per cell length
    AdaptGradient { istep = 1 } { cmax = 1e-2 maxlevel = 8 minlevel = 6 } T
    
    OutputPPM { start = 0 } { convert ppm:- t-0.eps } { v = T }
    OutputPPM { start = 2.5 } { convert ppm:- t-2.5.eps } { v = T }
    OutputPPM { start = 5 } { convert ppm:- t-5.eps } { v = T }

    # Add a new variable 
    Variable Tref

    # Initialize Tref with the initial shape
    InitFraction { start = end } Tref (ellipse (0, -.236338, 0.2, 0.2))

    # Output the norms of the difference between T and Tref, stores that into
    # new variable DT
    OutputErrorNorm { start = end } norms { v = T } {
        s = Tref v = DT
    }

    OutputPPM { start = end } { convert ppm:- dt-5.eps } { v = DT }
}

• Time-reversed advection with curvature-based refinement

1 0 GfsAdvection GfsBox GfsGEdge {} {
    Time { end = 5 }
    Refine 8

    # Add tracer T, using a VOF advection scheme.
    # The default scheme is a Van-Leer limited, second-order upwind scheme.
    VariableTracerVOF T

    # Curvature K of the interface defined by T
    VariableCurvature K T

    InitFraction T (ellipse (0, -.236338, 0.2, 0.2))

    # Initialize U and V with the vortical shear flow field
    Init {} {
        U = sin((x + 0.5)*M_PI)*cos((y + 0.5)*M_PI)
        V = -cos((x + 0.5)*M_PI)*sin((y + 0.5)*M_PI)
    }

    # At t = 2.5 re-initialize U and V with the reversed flow field
    Init { start = 2.5 } { U = -U V = -V }
    
    # Adapt the mesh dynamically using a custom cost function returning
    # the cell size times the local curvature (only for cells cut by
    # the interface).
    # The maximum cost is set to 0.1 i.e. the radius of curvature must be
    # resolved with at least 10 cells.
    AdaptFunction { istep = 1 } { cmax = 0.1 maxlevel = 8 minlevel = 6 } {
        return T > 0. && T < 1. ? ftt_cell_size (cell)*fabs (K) : 0.;
    }

    OutputSimulation { start = 2.5 } stdout
    EventScript { start = 2.5 } { echo "Save t-2.5.eps { format = EPS line_width = 0.5 }" }
    
    # Add a new variable 
    Variable Tref

    # Initialize Tref with the initial shape
    InitFraction { start = end } Tref (ellipse (0, -.236338, 0.2, 0.2))

    # Output the norms of the difference between T and Tref, stores that into
    # new variable DT
    OutputErrorNorm { start = end } norms { v = T } {
        s = Tref v = DT
    }

    OutputPPM { start = end } { convert ppm:- dt-5.eps } { v = DT }
}