vector_lowvisc

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vector_lowvisc

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{  VECTOR_LOWVISC.PDE

 

 This example is an implementation of LOWVISC.PDE using vector variables.

 

}

title 'Viscous flow in 2D channel, Re > 40'

select errlim = 0.005

variables

  vel(0.01) = vector(u,v)

  p(1)

definitions

  Lx = 5       Ly = 1.5

  Gx = 0       Gy = 0

  p0 = 2

  speed2 = u^2+v^2

  speed = sqrt(speed2)

  dens = 1

  visc = 0.04

  vxx = (p0/(2*visc*(2*Lx)))*(Ly-y)^2     { open-channel x-velocity }

  rball=0.25

  cut = 0.05       { bevel the corners of the obstruction }

  penalty = 100*visc/rball^2

  Re = globalmax(speed)*(Ly/2)/(visc/dens)

initial values

  vel = vector(0.5*vxx ,0)

  p = p0*x/(2*Lx)

equations

  vel:  visc*div(grad(vel)) - grad(p) = dens*dot(vel,grad(vel))

  p:  div(grad(p)) = penalty*div(vel)

Boundaries

  region 1

    start(-Lx,0)

    load(u) = 0   value(v) = 0   load(p) = 0

      line to (Lx/2-rball,0)

    value(vel)=vector(0,0) load(p)= 0

      line to (Lx/2-rball,rball) bevel(cut)

            to (Lx/2+rball,rball) bevel(cut)

            to (Lx/2+rball,0)

    load(u) = 0 value(v) = 0 load(p) = 0

      line to (Lx,0)

    load(u) = 0 value(v) = 0 value(p) = p0

      line to (Lx,Ly)

    value(vel)=vector(0,0) load(p) = 0

      line to (-Lx,Ly)

    load(u) = 0 value(v) = 0 value(p) = 0

      line to close

monitors

  contour(speed)

plots

  contour(u) report(Re)

  contour(v) report(Re)

  contour(speed) painted report(Re)

  vector(u,v) as "flow" report(Re)

  contour(p) as "Pressure" painted

  contour(dx(u)+dy(v)) as "Continuity Error"

  elevation(u) from (-Lx,0) to (-Lx,Ly)

  elevation(u) from (0,0) to (0,Ly)

  elevation(u) from (Lx/2,0) to (Lx/2,Ly)

  elevation(u) from (Lx,0) to (Lx,Ly)

end