A pressure-based algorithm for multi-phase flow at all speeds

“…Indeed, pressure correction schemes are partly implicit, thereby ensuring some stability with respect to the time step together with introducing a decoupling of the equations which helps the numerical solution of the nonlinear systems. Extensions to multi-phase flows are scarcer and seem to be restricted to iterative algorithms, often similar in spirit to the usual SIMPLE algorithm for incompressible flows [27,22,20]. In this paper, we perform a numerical study of a non-iterative pressurecorrection scheme introduced in [10], based on a low order finite element and a finite volume discretization, which enjoys the following properties:…”

Section: Introductionmentioning

confidence: 99%

Pressure correction staggered schemes for barotropic one-phase and two-phase flows

Kheriji¹,

Herbin²,

Latché³

2013

Computers & Fluids

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SummaryWe assess in this paper the capability of a pressure correction scheme to compute shock solutions of the homogeneous model for barotropic two-phase flows. This scheme is designed to inherit the stability properties of the continuous problem: the unknowns (in particular the density and the dispersed phase mass fraction y) are kept within their physical bounds, and the entropy of the system is conserved, thus providing an unconditional stability property. In addition, the scheme keeps the velocity and pressure constant through contact discontinuities. These properties are obtained by coupling the mass balance and the transport equation for y in an original pressure correction step. The space discretization is staggered; the numerical schemes which are considered are the Marker-And Cell (MAC) finite volume scheme and the nonconforming low-order Rannacher-Turek and Crouzeix-Raviart finite element approximation. In either case, a finite volume technique is used for all convection terms. Numerical experiments performed here show that, provided that a sufficient dissipation is introduced in the scheme, it converges to the (weak) solution of the continuous hyperbolic system. Observed orders of convergence for 1D Riemann problems as a function of the mesh and time step at constant CFL number vary with the studied case, and the CFL number and on the regularity of the solution. They range from 0.5 to greater than 1 for the velocity and the pressure; in most cases, the density and mass fraction converge with a 0.5 order. Finally, the scheme shows a satisfactory behaviour up to large CFL numbers.

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“…The ÿrst area has been recently the subject of a number of papers by the authors [6,7], and the reader is referred to a recent review of all-speed multi-uid ow algorithms [8] that includes several sections on robustness improvement techniques as well as a set of new algorithms capable of resolving the diverse pressure-velocity-density-volume fraction couplings.…”

Section: Introductionmentioning

confidence: 99%

“…This paper describes an extension of the full approximation storage full multi-grid (FAS-FMG) [14,20] algorithm to a recently developed all-speed multi-uid ow algorithm based on global mass conservation [7]. A number of implementation issues are addressed, such as the use of special inter-grid transfer operators to maintain the realizability of the solution and the special treatment of the volume fraction equation during prolongation.…”

Section: Introductionmentioning

confidence: 99%

A robust multi‐grid pressure‐based algorithm for multi‐fluid flow at all speeds

Darwish

Moukalled

Sekar

2003

Numerical Methods in Fluids

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SUMMARYThis paper reports on the implementation and testing, within a full non-linear multi-grid environment, of a new pressure-based algorithm for the prediction of multi-uid ow at all speeds. The algorithm is part of the mass conservation-based algorithms (MCBA) group in which the pressure correction equation is derived from overall mass conservation. The performance of the new method is assessed by solving a series of two-dimensional two-uid ow test problems varying from turbulent low Mach number to supersonic ows, and from very low to high uid density ratios. Solutions are generated for several grid sizes using the single grid (SG), the prolongation grid (PG), and the full non-linear multi-grid (FMG) methods. The main outcomes of this study are: (i) a clear demonstration of the ability of the FMG method to tackle the added non-linearity of multi-uid ows, which is manifested through the performance jump observed when using the non-linear multi-grid approach as compared to the SG and PG methods; (ii) the extension of the FMG method to predict turbulent multi-uid ows at all speeds. The convergence history plots and CPU-times presented indicate that the FMG method is far more e cient than the PG method and accelerates the convergence rate over the SG method, for the problems solved and the grids used, by a factor reaching a value as high as 15.

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A pressure-based algorithm for multi-phase flow at all speeds

Cited by 36 publications

References 65 publications

A coupled model for simulation of the gas–liquid two-phase flow with complex flow patterns

A coupled model for simulation of the gas–liquid two-phase flow with complex flow patterns

Pressure correction staggered schemes for barotropic one-phase and two-phase flows

A robust multi‐grid pressure‐based algorithm for multi‐fluid flow at all speeds

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