farfield boundary condition for external flow problems (flow around bodies)

[Walter]

Hi, everyone!

Problem description

I want to use dugksFoam to calculate the low-speed incompressible flow passing a micro-cylinder. I found cases like internal flow problems (only wall boundary condition is needed) and supersonic flow around a body in the user guide and published papers using dugksFoam, so I decided to try a supersonic-flow-around-a-2-D-cylinder case first. The case appears in Discrete unified gas kinetic scheme on unstructured meshes.

However, the description of the farfield BC in the user guide is a bit vague, which reads: "To specify such a boundary type, just set the boundary types as fixedValue, and provide the free-stream flow condition as the boundary values in 0/rho, 0/U and 0/T." If the velocity on the whole outer boundary is set to fixedValue, how can the flow field adjust to a steady state? I tried setting the BC as the user guide suggested, but the solving soon diverged. I changed fixedValue to farField; the solving has not diverged yet but the result is weird.

So, how should I specify the farfield BC?
Can dugksFoam be used to calculate the incompresible external flow problem?
(I post this issue in parallel-cdugksFoam at first. Hope it doesn't bother and many thanks.)

Details of the settings

fvDVMparas
{
    xiMax       xiMax [0 1 -1 0 0 0 0]    5.053155000000000e+03;
    xiMin       xiMin [0 1 -1 0 0 0 0]   -5.053155000000000e+03;
    nDV               89;       // Number of discrete velocity, shoud be 4*Z + 1 if using compound N-C quardrature
}

gasProperties
{
    R            R [0 2 -2 -1 0 0 0] 207.85; // Specific gas constant
    omega        0.81;              // VHS viscosity ~ Temperature index
    Tref         Tref [0 0 0 1 0 0 0] 273.0; // Reference temperature
    muRef        muRef [1 -1 -1 0 0 0 0] 2.117e-5;
    Pr           0.6667; // Prantl number
}

0/U

boundaryField
{
    cylinder
    {
        type            fixedValue;
        value           uniform (0 0 0);
    }
    farfield
    {
        type            farField;
        value 		uniform (1538.73 0 0);        
    }
    frontAndBack
    {
        type            empty;
    }
}

0/T

boundaryField
{
    cylinder
    {
        type            fixedValue;
        value           uniform 273;
    }
    farfield
    {
        type            farField;
        value           uniform 273;
    }
    frontAndBack
    {
        type            empty;
    }
}

0/rho

boundaryField
{
    cylinder
    {
        type            calculatedMaxwell;
        value           uniform 8.598e-5;  // dummy
    }
    farfield
    {
        type            farField;
        value           uniform 8.598e-5;
    }
    frontAndBack
    {
        type            empty;
    }
}

Result

The solution time interval is about 2e-8, and the flow fields of , , and at 3e-4