A multigrid solver for the coupled pressure-temperature equations in an all-Mach solver with VoF

We present a generalisation of the all-Mach solver of Fuster and Popinet (2018) [1] to account for heat diffusion between two different compressible phases. By solving a two-way coupled system of equations for pressure and temperature, the current code is shown to increase the robustness and accuracy of the solver with respect to classical explicit discretization schemes. Different test cases are proposed to validate the implementation of the thermal effects: an Epstein-Plesset like problem for temperature is shown to compare well with a spectral method solution. The code also reproduces free small amplitude oscillations of a spherical bubble where analytical solutions capturing the transition between isothermal and adiabatic regimes are available. We show results of a single sonoluminescent bubble (SBSL) in standing waves, where the result of the DNS is compared with that of other methods in the literature. Moreover, the Rayleigh collapse problem is studied in order to evaluate the importance of thermal effects on the peak pressures reached during the collapse of spherical bubbles. Finally, the collapse of a bubble near a rigid boundary is studied reporting the change of heat flux as a function of the stand-off distance.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

We extend the all-Mach solver proposed by Fuster and Popinet (2018) [1] to account for heat diffusion between two compressible phases. By solving a coupled system of equations for pressure and temperature, our code improves the robustness and accuracy of the solver compared to classical explicit discretization schemes. Several test cases are used to validate the implementation, including comparisons with spectral methods and analytical solutions. The code is also applied to the study of sonoluminescent bubbles, Rayleigh collapse, and bubble collapse near a rigid boundary, demonstrating the importance of thermal effects in these phenomena.