sandbox/fuster/README

My personal sandbox

Regularization methods (one fluid model)

Currently I am working on the impact of regularization errors introduced by the one-fluid formulation.

• For elliptic equations two works are already published: In absence of jumps JCP, 2024 and in the presence of jumps JCP,2025

• More recently, we have evaluated the impact of regularization errors on the development of interfacial instabilities Aknine et al, 2026

Development of AMR methods

Within the PhD of Lucas Prouvost and in collaboration with Anca Belme, we have been working on a metric based AMR method that we have implemented in Basilisk. Check his PhD manuscript and PhD defense. You can find the codes and some results in Lucas’ sandbox.

Tests and examples for the All-Mach formulation

List of tests and examples of the all-Mach compressible solver Fuster and Popinet (JCP, 2018). This includes thermal effects implemented by Saade et al JCP, 2023 see his sandbox

The code is now part of the stable release, so you can check the test cases included in the last version of Basilisk here

Related works

• The work from the PhD of Mandeep Saini which includes:

  • On the dynamics of a collapsing bubble in contact with a rigid wall (JFM)

  • Direct numerical simulations of microlayer formation during heterogeneous bubble nucleation (JFM)

  • A Review of the Accuracy of Direct Numerical Simulation Tools for the Simulation of Non-Spherical Bubble Collapses (JISS)

  • Finite speed of sound effects on asymmetry in multibubble cavitation (PRF)

    Check Saini’s sandbox for more information.

• Finite amplitude wave propagation through bubbly fluids Ohl et al, IJMF, 2024

• Effects of surface tension on the Richtmyer-Meshkov instability in fully compressible and inviscid fluids. Tang et al PRF, 2021

• Optimal subharmonic emission of stable bubble oscillations in a tube Fan et al, PRE, 2020