Regarding checkerboard pressure and momentum in two-phase-compressible

[Shyam Sunder Yadav]

Dear All

I am trying to simulate single phase compressible flow of water in sudden expansion and contraction kind of geometries with the help of two-phase-compressible.h and all-mach.h solvers.

I modified the Mach 3 wind tunnel example from Dr. Fuster's sandbox: http://basilisk.fr/sandbox/fuster/Allmach3.0/stepAllMach.c

I am getting checkerboard pressure and momentum fields as shown in the attached screenshots. I am using the minmod2 limiter.

The files I am using are attached with this mail. I am using an older version of Basilisk, the file output_hdf.h may need to be corrected in the newer versions.

I request you kindly give me some hints on how to improve the solution.

A basic analysis of the all-mach.h header shows the following code at line 237

----------------------------------------------------------------------------------------

  /** We also compute the combined face pressure gradient and acceleration
  field *gf*. */

  face vector gf[];
  foreach_face() {
    double dp = alpha.x[]*(p[] - p[-1])/Delta;
    uf.x[] -= dt*dp;
    gf.x[] = a.x[] - dp/fm.x[];
  }

  /**
  And finally we apply the pressure gradient/acceleration term to the
  flux/momentum. We also store the centered, combined pressure
  gradient and acceleration field *g*. */
 
  foreach()
    foreach_dimension() {
    g.x[] = rho[]*(gf.x[] + gf.x[1])/(2.*cm[]);
    q.x[] += dt*g.x[];
  }

----------------------------------------------------------------------------------------

We are basically calculating face pressure gradient by central differencing and from that the cell centered pressure gradient by simple averaging.

This averaged pressure gradient then drives the momentum. The point to note is

that the pressure from the central most grid cell is not appearing and two independent pressure and velocity solutions may evolve.

Please point if I am wrong here.

Thank you.

Regards

--

Dr. Shyam Sunder Yadav
Assistant Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

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[Shyam Sunder Yadav]

To all those people struggling with two-phase-compressible flow with spurious oscillations in pressure, velocity, sudden inflow from outlets

================================================================================================================

Applying wave transmissive boundary condition for pressure at the outlet improves the simulation...

Check this document: https://hal.archives-ouvertes.fr/hal-01699049

That is: "Navier-Stokes Characteristic Boundary Conditions Using Ghost Cells" by Motheau et al.

Best wishes

[Wenge Huang]

Hi Dr. Shyam Sunder Yadav,

I'm now struggling with the spurious oscillation in the two-phase-compressible flow. Can you provide more details about how to apply the "wave transmissive boundary condition" in Basilisk. Thank you very much. 

[Shyam Sunder Yadav]

Dear All

I could not resolve this problem of characteristic boundary conditions. 

In the process, I compiled some information in the form of attached slides which I use for covering the topic in my CFD class.

Most of the information is directly copy-pasted from various sources. Nothing is mine. I apologize for that in advance.

I hope these will be useful.

Regards

Dr. Shyam Sunder Yadav
Associate Professor

Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile