Subject: Spurious currents for 3D sessile droplet at high density ratio (water/air)
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Kevin Ripamonti
Apr 3, 2026, 3:21:03 AM (yesterday) Apr 3
to basilisk-fr
Dear Basilisk community,
I am simulating a 3D sessile water droplet (5 µl, R = 1.34 mm, contact angle 100°) on a flat substrate with the goal of applying a weak body force (SAW acoustic streaming, ~0.02-0.05 m/s) and comparing with published LBM results (Burnside et al., Phys. Rev. E 104, 2021), to validate the fluidodinamic model before implementing the SAW for acoustic streaming through metamaterials.
The problem: at the real water/air density ratio (~830:1), I cannot reduce spurious currents below ~5e-3 m/s (with 100x viscosity multiplier) regardless of resolution or approach. This is comparable to the physical streaming velocity I need to resolve.
I have systematically tested the following configurations (all 3D octree, ML=7-8):
1. two-phase.h + contact.h (h.t + h.r) + tension.h → plateau ~0.01 m/s
2. Adding #define FILTERED + reduced.h + navier-stokes/conserving.h → plateau ~0.005 m/s
3. Adding stokes=true → spurious currents drop monotonically to 3e-4 then RISE BACK to ~3e-3 and become oscillatory
4. Embedded boundary (embed.h + contact-embed.h from sandbox/tavares) without AMR → oscillations 5e-4 to 6e-3, no convergence
5. #define JACOBI 1, TOLERANCE=1e-8, NITERMIN=2 → same behavior as (3)
The adapt trick from sessile3D.c (smooth f copy for AMR) is used in all cases.
I notice that sessile.c, sessile3D.c and spurious.c all use density ratio 1:1. At 1:1, machine accuracy is achieved. The issue appears fundamental to high density ratios: pressure errors at the interface produce accelerations ~830x larger in the gas phase.
The curious behavior in case (3) — monotonic decrease to 3e-4 followed by systematic rise — suggests an instability mechanism at the contact line that is suppressed by viscous damping during the initial transient but grows once the velocity field is small enough.
My questions:
- Is there a known approach in Basilisk to achieve low spurious currents for static sessile droplets at realistic water/air density ratios?
- Has anyone successfully simulated static equilibrium of a sessile droplet at density ratio >100 with spurious currents converging to zero?
- Would the double-projection scheme help with this specific issue?
Physical parameters: rho_l=998.2, rho_g=1.2, mu_l=1e-3 (×100 during relaxation), mu_g=1.8e-5 (×100), sigma=0.07273 N/m, g=9.81 m/s².
Thank you for any insight.
Kevin Ripamonti
I am simulating a 3D sessile water droplet (5 µl, R = 1.34 mm, contact angle 100°) on a flat substrate with the goal of applying a weak body force (SAW acoustic streaming, ~0.02-0.05 m/s) and comparing with published LBM results (Burnside et al., Phys. Rev. E 104, 2021), to validate the fluidodinamic model before implementing the SAW for acoustic streaming through metamaterials.
The problem: at the real water/air density ratio (~830:1), I cannot reduce spurious currents below ~5e-3 m/s (with 100x viscosity multiplier) regardless of resolution or approach. This is comparable to the physical streaming velocity I need to resolve.
I have systematically tested the following configurations (all 3D octree, ML=7-8):
1. two-phase.h + contact.h (h.t + h.r) + tension.h → plateau ~0.01 m/s
2. Adding #define FILTERED + reduced.h + navier-stokes/conserving.h → plateau ~0.005 m/s
3. Adding stokes=true → spurious currents drop monotonically to 3e-4 then RISE BACK to ~3e-3 and become oscillatory
4. Embedded boundary (embed.h + contact-embed.h from sandbox/tavares) without AMR → oscillations 5e-4 to 6e-3, no convergence
5. #define JACOBI 1, TOLERANCE=1e-8, NITERMIN=2 → same behavior as (3)
The adapt trick from sessile3D.c (smooth f copy for AMR) is used in all cases.
I notice that sessile.c, sessile3D.c and spurious.c all use density ratio 1:1. At 1:1, machine accuracy is achieved. The issue appears fundamental to high density ratios: pressure errors at the interface produce accelerations ~830x larger in the gas phase.
The curious behavior in case (3) — monotonic decrease to 3e-4 followed by systematic rise — suggests an instability mechanism at the contact line that is suppressed by viscous damping during the initial transient but grows once the velocity field is small enough.
My questions:
- Is there a known approach in Basilisk to achieve low spurious currents for static sessile droplets at realistic water/air density ratios?
- Has anyone successfully simulated static equilibrium of a sessile droplet at density ratio >100 with spurious currents converging to zero?
- Would the double-projection scheme help with this specific issue?
Physical parameters: rho_l=998.2, rho_g=1.2, mu_l=1e-3 (×100 during relaxation), mu_g=1.8e-5 (×100), sigma=0.07273 N/m, g=9.81 m/s².
Thank you for any insight.
Kevin Ripamonti
Shyam Sunder Yadav
Apr 3, 2026, 3:49:20 AM (yesterday) Apr 3
to Kevin Ripamonti, basilisk-fr
Dear Kevin
The spurious velocity current issue is hard to resolve...
You can further try the CLSVOF method with the integral formulation for surface tension...
You have to extend the surface tension formulation to 3D, I don't know whether someone has tried it...
Best wishes
Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile
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Kevin Ripamonti
Apr 3, 2026, 8:27:56 AM (yesterday) Apr 3
to basilisk-fr
Dear Dr. Yadav,
Thank you very much for your suggestion. The CLSVOF + integral formulation approach is very interesting and I will definitely investigate it.
Before implementing it, I would like to understand better why this method should perform better specifically at high density ratios. From my understanding, the integral formulation provides a smoother curvature calculation (from the level set distance function) and a structurally better-balanced surface tension representation. This should reduce the source of spurious currents.
However, the amplification mechanism seems to remain: in the Navier-Stokes equations, any residual imbalance between the pressure gradient and the surface tension force produces an acceleration proportional to 1/rho. In the gas phase (rho ~ 1.2 kg/m3), this amplification factor is ~830x larger than in the liquid. This amplification is independent of how the surface tension is computed.
Do you have experience or references showing that the integral formulation specifically addresses this density-ratio amplification? Or is the improvement mainly through a much more accurate curvature computation that reduces the residual at the source?
Thank you again for your time and insight.
Best regards,
Kevin
Thank you very much for your suggestion. The CLSVOF + integral formulation approach is very interesting and I will definitely investigate it.
Before implementing it, I would like to understand better why this method should perform better specifically at high density ratios. From my understanding, the integral formulation provides a smoother curvature calculation (from the level set distance function) and a structurally better-balanced surface tension representation. This should reduce the source of spurious currents.
However, the amplification mechanism seems to remain: in the Navier-Stokes equations, any residual imbalance between the pressure gradient and the surface tension force produces an acceleration proportional to 1/rho. In the gas phase (rho ~ 1.2 kg/m3), this amplification factor is ~830x larger than in the liquid. This amplification is independent of how the surface tension is computed.
Do you have experience or references showing that the integral formulation specifically addresses this density-ratio amplification? Or is the improvement mainly through a much more accurate curvature computation that reduces the residual at the source?
Thank you again for your time and insight.
Best regards,
Kevin
Shyam Sunder Yadav
Apr 3, 2026, 11:44:23 AM (yesterday) Apr 3
to Kevin Ripamonti, basilisk-fr
Sorry Kevin...I don't have experience in this area...
I myself am struggling with spurious velocity currents with phase field methods...
I am dealing with air, water and ice properties...so high density ratio and high surface tensions...
Definitely Prof. Zaleski and Prof. Popinet can suggest something...
Regards
Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile
To view this discussion visit https://groups.google.com/d/msgid/basilisk-fr/a5933863-9c19-4d70-a4ec-adc294498d02n%40googlegroups.com.
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