V&V » LohCG: Inviscid flow past a sphere

This example uses LohCG in Inciter to compute the inviscid constant-density (incompressible) flow past a sphere. Since the analytic solution of this problem is known from potential flow theory, we can use it to verify the correctness of the software implementation of the method.

Problem setup

Due to the spatial symmetry of the problem, only quarter of the sphere is represented. The computational mesh consists of 73,397 tetrahedra connecting 14,281 points, whose surface mesh is depicted below. The initial conditions prescribe the free-stream velocity of $\mbox{\boldmath$v$}=(1,0,0)$ . As boundary conditions, the pressure is set to zero at the outflow and the velocity is set to $\mbox{\boldmath$v$}=(1,0,0)$ at the inflow. Symmetry (free-slip) conditions are applied on the sphere, the symmetry and farfield surfaces.

Image

Code revision to reproduce

To reproduce the results below, use code revision d4d1f48 and the control file below.

Control file

-- vim: filetype=lua:

print "Inviscid quarter sphere"

-- mesh: sphere_quarter.exo

term = 0.3
ttyi = 100

cfl = 1.0

solver = "lohcg"
flux = "damp4"
stab2 = true
stab2coef = 0.1
soundspeed = 50.0
rk = 4

part = "phg"

pressure = {
  iter = 300,
  tol = 1.0e-4,
  --verbose = 1,
  pc = "jacobi",
  bc_dir = { { 7, 1 } }
}

ic = {
  velocity = { 1.0, 0.0, 0.0 }
}

bc_dir = {
  { 6, 0, 1, 1, 1 },
  { 7, 1, 0, 0, 0 }
}

bc_sym = {
  sideset = { 1, 2, 3, 4, 5 }
}

fieldout = {
  iter = 1000,
  sideset = { 1, 2, 3 }
}

diag = {
  iter = 1,
  format = "scientific",
  precision = 12
}

Run on a single CPU

Main/inciter -i sphere_quarter.exo -c sphere_lohcg_inviscid_quarter.q

Visualization and numerical results

ParaView can be used for interactive visualization of the numerically computed 3D fields as

paraview out.e-s.0.1.0

The velocity magnitude along the X axis following the sphere surface is depicted below.

Image