A Robust All-Mach Six-Equation Diffuse-Interface Method for Multiphase Flows with Surface Tension
Abstract
A robust finite-volume framework is presented for the simulation of compressible multiphase flows with surface tension across a wide range of Mach numbers. The method is based on a two-pressure, six-equation diffuse interface model incorporating viscous, gravitational, and capillary effects through the continuum surface force formulation. To consistently account for capillary-induced pressure jumps, an HLLC Riemann solver is developed using generalized Riemann invariant analysis, and the instantaneous pressure relaxation procedure is modified to preserve the Laplace pressure jump during phase equilibration. To overcome the excessive numerical diffusion of conventional approximate Riemann solvers in the low-Mach regime, a robust low-Mach correction is proposed by extending our previous formulation with a modified scaling strategy that remains stable in regions of strong pressure variation. The resulting method retains accuracy from nearly incompressible flows to compressible regimes while preserving the robustness of the six-equation formulation. The numerical framework is validated using a series of benchmark problems involving surface tension, viscosity, gravity, and compressibility. The results demonstrate accurate prediction of interface dynamics, capillary pressure, and low-Mach flow features, while significantly reducing numerical dissipation without compromising stability. The proposed methodology provides an efficient and reliable approach for the simulation of complex multiphase flows spanning a broad range of flow regimes.
Related
- Variational formulation of the constitutive relaxation at finite rate of the mechanical state in multiphase flows with the diffuse-interface method
- Simultaneous Sharp-Interface Limits for a Diffuse-Interface Landau--de Gennes Droplet Model
- Local Well-posedness of a Diffuse Interface Two-phase Flow Model with Surfactants
- Well-posedness of Strong Solutions for a Thermodynamically Consistent Diffuse-interface Model for Incompressible Two-phase Flows with a Soluble Surfactant
- Enhanced lifespan of solutions to Whitham-Boussinesq system with surface tension
BibTeX
@misc{bharate2026robust,
title = {{A Robust All-Mach Six-Equation Diffuse-Interface Method for Multiphase Flows with Surface Tension}},
author = {Ghanshyam Bharate and J. C. Mandal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10727},
eprint = {2609.10727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10727},
}
RIS
TY - UNPB
TI - A Robust All-Mach Six-Equation Diffuse-Interface Method for Multiphase Flows with Surface Tension
AU - Ghanshyam Bharate
AU - J. C. Mandal
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10727
UR - https://arxiv.org/abs/2609.10727
AB - A robust finite-volume framework is presented for the simulation of compressible multiphase flows with surface tension across a wide range of Mach numbers. The method is based on a two-pressure, six-equation diffuse interface model incorporating viscous, gravitational, and capillary effects through the continuum surface force formulation. To consistently account for capillary-induced pressure jumps, an HLLC Riemann solver is developed using generalized Riemann invariant analysis, and the instantaneous pressure relaxation procedure is modified to preserve the Laplace pressure jump during phase equilibration. To overcome the excessive numerical diffusion of conventional approximate Riemann solvers in the low-Mach regime, a robust low-Mach correction is proposed by extending our previous formulation with a modified scaling strategy that remains stable in regions of strong pressure variation. The resulting method retains accuracy from nearly incompressible flows to compressible regimes while preserving the robustness of the six-equation formulation. The numerical framework is validated using a series of benchmark problems involving surface tension, viscosity, gravity, and compressibility. The results demonstrate accurate prediction of interface dynamics, capillary pressure, and low-Mach flow features, while significantly reducing numerical dissipation without compromising stability. The proposed methodology provides an efficient and reliable approach for the simulation of complex multiphase flows spanning a broad range of flow regimes.
ER -