GfsSourceViscosity

From Gerris

GfsSourceViscosity solves the diffusion equation for the velocity (a vector quantity obviously) while GfsSourceDiffusion solves the diffusion equation for a scalar quantity. In the case of a spatially uniform viscosity the two are strictly equivalent since — in the case of an incompressible fluid — the vector diffusion equation for the velocity can be split in independent scalar diffusion equations for each of the Cartesian components of the velocities.

To sum up, using GfsSourceViscosity is safe in all cases, regardless of whether the viscosity is uniform.

The syntax in parameter files is:

[ GfsSourceVelocity ] [ GfsDiffusion ]

Examples

• Rayleigh-Taylor instability

  SourceViscosity {} 0.00313

• Viscous flow past a sphere

    SourceViscosity 1./RE

• Poiseuille flow

    SourceViscosity 1. { beta = 1 }

• Creeping Couette flow of Generalised Newtonian fluids

  SourceViscosity {} {
    double mu, ty, N, mumax = 1000.;
    double m;

    switch (MODEL) {
    case 0: /* Newtonian */
      mu = 1.; ty = 0.; N = 1.; break;
    case 1: /* Power-law (shear-thinning) */
      mu = 0.08; ty = 0.; N = 0.5; break;
    case 2: /* Herschel-Bulkley */
      mu = 0.0672; ty = 0.12; N = 0.5; break;
    case 3: /* Bingham */
      mu = 1.; ty = 10.; N = 1.; break;
    }
    if (D2 > 0.)
      m = ty/(2.*D2) + mu*exp ((N - 1.)*log (D2));
    else {
      if (ty > 0. || N < 1.) m = mumax;
      else m = N == 1. ? mu : 0.;
    }
    return MIN (m, mumax);
  } {
    # Crank-Nicholson does not converge for these cases, we need backward Euler
    # (beta = 0.5 -> Crank-Nicholson, beta = 1 -> backward Euler)
    beta = 1
  }

• Momentum conservation for large density ratios

    SourceViscosity mu(T1)

• Hydrostatic balance with solid boundaries and viscosity

    SourceViscosity 1e-2

• Hydrostatic balance with quadratic pressure profile

    SourceViscosity 1e-2

• Axisymmetric spherical droplet in equilibrium

  SourceViscosity MU

• Air-Water capillary wave

  SourceViscosity 0.0182571749236*MU(T1)