V&V » LohCG: Lid-driven cavity

This example uses LohCG in Inciter to compute the stationary viscous constant-density (incompressible) laminar flow field in a cubic domain driven by a shearing velocity on one side. The numerical solution is compared to those published in [1].

Problem setup

The problem domain is a cube with 5 solid walls and a constant shear-velocity prescribed on the 6th one. The mesh consts of 750,000 tetrahedra connecting 132,651 pointsis, displayed below. The initial conditions prescribe a quiescent state with $\mbox{\boldmath$v$}(\mbox{\boldmath$x$},t=0)=(0,0,0)$ . The boundaries at walls prescribe no-slip/no-penetration with $\mbox{\boldmath$v$}(t)=(0,0,0)$ . The shear velocity on top of the cube is enforced using a Dirichlet condition as $ \mbox{\boldmath$\overline{v}$}(t) = (1,0,0) $ . The dynamic viscosity is specified as $\mu=0.01$ , which yields a Reynolds number of $ \text{Re} = \rho \overline{v}_x L / \mu = 100 $ , defined based on the fluid density $\rho=1$ , the length of the cube $L=1$ , and the imposed shear velocity of $ \overline{v}_x = 1 $ .

Image Surface mesh for computing lid-driven cavity, nelem=750K, npoin=132K.

Code revision to reproduce

To reproduce the results below, use code revision 4c61fe1 and the control file below.

Control file

-- vim: filetype=lua:

print "Lid-driven cavity"

-- mesh: mms/unitcube_94K.exo
--       mms/unitcube_750K.exo
--       mms/unitcube_6M.exo
--       mms/unitcube_48M.exo

term = 40.0
ttyi = 1000

cfl = 0.9

solver = "lohcg"
flux = "damp2"
stab2 = true
stab2coef = 0.01
soundspeed = 1000.0
rk = 2

part = "rcb"

Re = 100.0
mat = { dyn_viscosity = 1.0/Re }

pressure = {
  iter = 500,
  tol = 1.0e-3,
  verbose = 1,
  pc = "jacobi",
  hydrostat = 0
}

ic = {
  velocity = { 0.0, 0.0, 0.0 }
}

bc_noslip = {
  sideset = { 1, 2, 3, 5, 6 }
}

bc_dir = {
  { 4, 0, 2, 2, 2 }
}

bc_dirval = {
  { 4, 0.0, 1.0, 0.0, 0.0 }
}

fieldout = {
  iter = 100000
}

diag = {
  iter = 100,
  format = "scientific",
  precision = 12
}

Run on 64 CPUs

./charmrun +p64 Main/inciter -i unitcube_750K.exo -c ldc_lohcg.q

Numerical solution

Plotted below are the computed velocity profiles sampled in the middle of the domain along lines in the X and Y directions, obtained after the solution has converged to a stationary state. The numerical solution is compared to those in [1].

Image Image

References

  1. U. Ghia, K.N. Ghia, and C.T. Shin, High-Re Solutions of Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method, Journal of Computational Physics, 48(3), 387-411, 1982.