Numerical algorithms for two-fluid, weakly-compressible flows
Date
2024
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Abstract
A multifluid numerical method is developed for flows of two fluids in a single domain at low Mach numbers. An all-speed formulation of the Navier-Stokes equations governs the dynamics of both fluids and the level-set method defines the interface between them and the domain of each fluid. The algorithm represents velocity and pressure as single valued throughout the whole domain, and fluid dependent variables, density and bulk modulus, only in the domain of their respective fluid. The all-speed equations are not subject to the divergence-free velocity constraint through use of a redundant velocity equation, and are evolved in time using an implicit-explicit additive Runge-Kutta method resulting in a time step constrained only by the bulk fluid velocity. Each fluid is evolved conservatively with respect to the moving interface between them. Due to errors in the evolution in the interface, perturbations in the volume of each fluid, and thereby the density, can develop. A thermodynamically consistent correction is made to the position of the interface to reduce these unphysical perturbations. The algorithm developed here includes three novel contributions: (i) the use of a multifluid all-speed algorithm with a level-set method for evolution of the solution in time, (ii) a multifluid algorithm using the level-set to capture the interface in the weakly compressible regime that is thermodynamically consistent, and (iii) an initialization method for sharp corners in the level-set. Numerical tests have demonstrated that the algorithm exhibits the expected low Mach number behavior, achieves second order-accuracy, and ensures fluid volumes are bounded and convergent.
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Subject
level-set
multifluid
low Mach number
all-speed