An all-speed relaxation scheme for interface flows with surface tension

Liquid and liquid–gas flows at all speeds

“…These two formulas are identical to those given by Murrone and Guillard [45] and Braconnier and Nkonga [46]. However, the Mach number is calculated with the sound speed (26).…”

“…The HLLC Riemann solver of Toro et al [34] is considered and wave speeds for all Mach number flow situations are estimated following Murrone and Guillard [45] and Braconnier and Nkonga [46] with the help of the following analysis. For the approximate Riemann problem resolution only (not for the solution update), the Euler equations are considered under primitive variables formulation: ∂ρ ∂t…”

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

“…This has inspired development of multiphase models for chemically reacting and cavitating flows [25][26][27][28][29], including relaxation methods [30][31][32] which are derived from the general non-equilibrium models [33][34][35][36]. These methods can also be adapted to account for the effects of gravity and surface tension [37,38] and have been extended to model two vastly different phases such as solid and gas [39].…”

A pressure-based method for solving low Mach number two-phase flows with surface tension

“…Although this term plays a role to keep the thermodynamic consistency which corresponds to the velocity-mechanical equilibrium, it does not prevent the present model from taking over the oscillation-free property of the γ-based model for the well-known interface advection problem (Ooida et al, 2013). Furthermore, we note that the present model is similar to Braconnier and Nkonga (2009), except for solving Γ instead of α k (note that Γ and α k are replaceable by Eq. (5)) and including the irreversible effects in the evolution equation.…”