Non-boussinesq low mach number (LMN)

[alexandr...@gmail.com]

Dear All,

I just wanted to know, If someone had try to simulate non-Boussinesq flow with Basilisk ?

A Chebyshev collocation algorithm for 2D non-Boussinesq convection

(Gaz)

A 3D Low Mach Number model for high performance computations in natural or mixed convection newtonian liquid flows

(Liquid)

Do you think it's possible to use all-mach.h ?

Because, it seems that the pressure correction is different between all-mach.h and LMN.

Thank you,

Best regards

Alexandre

[Edoardo Cipriano]

Hello Alexandre,

Let me take this opportunity to advertise my recent work, though it may not be exactly what you're looking for.

I recently published a low-Mach VOF model to simulate droplet evaporation in buoyancy-driven flows:

https://dx.doi.org/10.1016/j.ijheatmasstransfer.2024.126115

For example, if you check this test case:

http://www.basilisk.fr/sandbox/ecipriano/run/normalgravity.c

You'll notice that the droplet evaporates, increasing the density in the surrounding region, which results in natural convective fluxes which create that downward velocity profile. This is captured without relying on the Boussinesq approximation.

This model is an extension of the incompressible framework, accounting for variable thermodynamic and transport properties, constant thermodynamic pressure (both in space and time), and volumetric sources in the continuity equation due to density changes.

The model has performed well in the test cases that I tried, which are those presented in the paper. While it was developed for two-phase flows, it could also be used for single-phase simulations (I’d be happy to share an example if you're interested, or I can upload one to the sandbox).

One key difference in the projection step between the low-Mach and all-Mach solvers is that, in the low-Mach approach, the thermodynamic pressure is assumed to be constant. This allows for neglecting pressure gradients in the continuity equations relative to temperature (and mass fraction) gradients, avoiding the two-way coupling between the energy and continuity equations discussed by Saade et al., 2023, in their work on the thermal extension of the all-Mach solver.

If you're particularly focused on the closed heated cavity problem, my model might require some extensions. Since I've only dealt with open systems, I neglected pressure variations, which would need to be incorporated for closed-cavity simulations with expansion terms. In such cases, a proper equation for the evolution of pressure must be included. In this work on the heated cavity problem, the authors include an equation for a spatially constant pressure which varies in time.

I haven’t worked with the all-Mach solver but it should, in principle, already combine pressure and thermal effects.

Cheers,

Edoardo

[alexandr...@gmail.com]

Hello Edoardo,

Thank you very much for your precise answer !

I'll be studying the different aspects of these models in more detail over the next few weeks, and trying to figure out what needs to be done with Basilisk.

I'll keep Basilisk users informed of what I've tried.

Best regards,

Alexandre