Accurate solution algorithms for incompressible multiphase flows

Rider, William J.; Kothe, Douglas B.; Mosso, Stewart John; Cerutti, John H.; Hochstein, John I.

doi:10.2514/6.1995-699

Cited by 53 publications

(53 citation statements)

References 39 publications

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“…The discrete-expansions in Equation 16 are combinations of transformation matrices and a higher-order interpolation derivative. Evaluation of the coordinate and geometry transformation matrices is easily visualized using Figure 3.…”

Section: Direct Integration Pathlinementioning

confidence: 99%

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Integrating a Bilinear Interpolation Function Across Quadrilateral Cell Boundaries

Brock¹

2001

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Computational models of particle dynamics often exchange solution data with discretized continuum-fields using interpolation functions. These particle methods require a series expansion of the interpolation function for two purposes: numerical analyses used to establish the models consistency and accuracy, and logical-coordinate evaluation used to locate particles within a grid.This report presents a new method of developing discrete-expansions for interpolation; they are similar to multi-variable expansions but, unlike a Taylor's series, discrete-expansions are valid throughout a discretized domain. Discrete-expansions are developed herein by parametrically integrating the interpolation function's total-differential between two particles located within separate, non-contiguous cells. Discrete-expansions are valid for numerical analyses since they acknowledge the functional dependence of interpolation and account for mapping discontinuities across cell boundaries. The use of discrete-expansions for logical-coordinate evaluation provides an algorithmically robust and computationally efficient particle localization method. Verification of this new method is demonstrated herein on a simple test problem.

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Section: Direct Integration Pathlinementioning

confidence: 99%

“…These methods include models of liquid sprays [1][2][3][4], wall-film dynamics [5][6][7][8], bubble dynamics [9][10][11][12][13], smoke dispersion [14], and material-interface tracking [15,16]. In contrast, reactive particles simply respond to the entraining fluid, and their governing equations are weakly coupled to the field equations.…”

Section: Introductionmentioning

confidence: 99%

Integrating a Bilinear Interpolation Function Across Quadrilateral Cell Boundaries

Brock¹

2001

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“…The experimental data of Rioboo, Marengo and Tropea (2002) are used for comparisons. The droplet-liquid impact problem (DLIP) is less well studied but in addition to the difficulties associated with the DSIP, this problem is ideal for studying the growth of instabilities which may arise over longer calculation times (Rider et al, 1995). The experimental data of Liow (2001) for a deep layer and of Josserand and Zaleski (2003) for a shallow layer are used for comparisons.…”

Section: Introductionmentioning

confidence: 99%

“…In the current method, these modes are damped through the use of iterated projection and velocity filters as discussed by Rider (1994). The MPFA, discussed in the previous paragraphs, has been shown to be an accurate, robust method of high fidelity (Rider et al, 1995). It has been used to solve constant density flow problems (Bell, Colella and Glaz, 1989), and has been extended to the variable density case (Bell and Marcus, 1992 , 1997), to solve two-phase flow problems.…”

Section: Introductionmentioning

confidence: 99%

“…One way to construct such a model, avoiding the awkward application of interfacial conditions among multiple flow solutions (Lakehal, Meier and Fulgosi, 2002), is to adopt the One-Field or single-domain approach (Anderson, McFadden and Wheeler, 1998; Scardovelli and Zaleski, 1999). All interacting fluid phases are now part of a single fluid (Vincent and Caltagirone, 2000; Rider et al, 1995) and velocity and pressure become global field variables. Bulk fluid properties, such as density and viscosity, remain constant within each phase but vary discontinuously across fluid interfaces.…”

Section: Introductionmentioning

confidence: 99%

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A Numerical Model for Multiphase Flow Based On The GMPPS Formulation, Part II: Dynamics

Bierbrauer¹,

Zhu²

2008

Engineering Applications of Computational Fluid Mechanics

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A numerical method for simulating variable density multiphase fluid flows is presented in this paper. It is a hybrid Eulerian-Lagrangian method solving the incompressible Navier-Stokes equations on a fixed Eulerian grid for velocity and pressure. Fluid phase is tracked in a Lagrangian manner by using marker-particles (Bierbrauer and Zhu, 2007a) to update the grid density and viscosity. A high order Godunov advection scheme, together with an approximate projection scheme to ensure incompressibility, is used to deal with rapid changes in fluid properties. We call this scheme the Godunov-Marker-Particle Projection Scheme (GMPPS), which implements pressure corrections to avoid spurious numerical boundary layers for multiphase flows. We have validated the GMPPS by comparing our numerical results with those calculated from an exact solution, with constant density, as well as some available physical experimental results for a variable density case. It is demonstrated that the scheme has secondorder accuracy in time and space for a range of Reynolds numbers. The fact that test results of a two-phase droplet impacting on solid and liquid surfaces compare well with experimental results suggests that the GMPPS has great potential to be used to solve multiphase flow problems.

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Volume-Tracking Methods for Interfacial Flow Calculations

Rudman

1997

Int. J. Numer. Meth. Fluids

667

417

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A new algorithm for volume tracking which is based on the concept of flux‐corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction‐split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the new scheme against well‐known existing 2D finite volume techniques is undertaken. A series of progressively more difficult advection tests is used to test the accuracy of each scheme and it is seen that simple advection tests are inadequate indicators of the performance of volume‐tracking methods. A straightforward methodology is presented that allows more rigorous estimates to be made of the error in volume advection and coupled volume and momentum advection in real flow situations. The volume advection schemes are put to a final test in the case of Rayleigh–Taylor instability. © 1997 by CSIRO.

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Accurate solution algorithms for incompressible multiphase flows

Cited by 53 publications

References 39 publications

Integrating a Bilinear Interpolation Function Across Quadrilateral Cell Boundaries

Integrating a Bilinear Interpolation Function Across Quadrilateral Cell Boundaries

A Numerical Model for Multiphase Flow Based On The GMPPS Formulation, Part II: Dynamics

Volume-Tracking Methods for Interfacial Flow Calculations

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