A fully segregated and unconditionally stable IMEX scheme for dispersed multiphase flows

October 24, 2025

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Key Points

The goal is to develop a stable and efficient scheme for simulating multiphase flows using the Navier–Stokes equations.
Derived a first-order pressure-correction method based on incompressibility of the mean velocity.
Explicit treatment of drag forces combined with semi-implicit handling of convective and viscous terms.
Implemented an implicit-explicit (IMEX) framework for computational efficiency.
Developed linear scalar transport equations and a pressure Poisson problem for each time step.
Proved unconditional energy stability without fixed-point iterations.
Demonstrated temporal stability with no requirement for CFL-like conditions.
Confirmed theoretical findings with numerical examples in a two-phase flow context.

This research introduces a novel IMEX method for modeling multiphase flows, addressing computational efficiency and stability.

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Pacheco et al. (2025) studied this question.

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