Volume-Tracking Methods for Interfacial Flow Calculations

Abstract

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.

Computational fluid dynamics applied to gas-liquid contactors

“…a region of the flow with high vorticity, it can clearly be seen that small bubbles are shed from the skirts of the bubble under consideration. This is most likely a limitation of the VOF approach, which is known to give inaccurate results for interfaces in a high shear flow (Kothc andRider, 1995 andRudman. 1997).…”

“…These methods use the NavierStokes equations to resolve the gas-phase and the liquid-phase velocity fields. The various Volume Tracking methods (Nichols et al, 1980;Hirt and Nichols, 1981;Youngs, 1982 andRudman, 1997) use a 'colour' function F to distinguish between the gas and the liquid phase, whereas Marker Particle methods such as the MAC method, use marker particles to track the time-dependent motion of the liquid phase. These Volume Tracking/Marker Particle methods can typically be used to provide in depth data on bubble coalescence, bubble break up and the shapes and sizes of bubbles under the prevailing flow conditions and physical properties of the liquid.…”

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

“…The VOF-type algorithms typically employ a segregated treatment for the system "flow variables -interface" and finite difference or finite volume approximations on fixed grids. For the review on state-of-the-art VOF-like methods one may be pointed to the papers Rudman (1997) and Scardovelli & Zaleski (1999) (see also Scardovelli & Zaleski (2003)). Some further references include the work Brackbill et al (1992) remarkable by its "continuum surface force" (CSF) approach proposed to include the surface tension into the right-hand side of momentum equation (see also Liovic et al (2002)) and the paper Lafaurie et al (1994) where the alternative "continuum surface stress" method was proposed within the finite volume framework (see also Wu et al (1998) for the implementation of the latter method in the combination with finite elements).…”

A General-Purpose Finite-Volume Advection Scheme for Continuous and Discontinuous Fields on Unstructured Grids

“…In the case of vortical shear flow, under time reversal, we show that we essentially recover the initial conditions. Error norms from these simulations on quadrilateral and triangular element meshes are tabulated along with those of [7,10]. Finally, we show a computation of advection of concentration in a jet flow field, which shows the efficacy and utility of our explicit-implicit formulation.…”

“…[3] 0.0069 FCT-VOF [7] 1.63e-8 Youngs [11] 0.0258 Ubbink and Issa, structured [10] 0.0250 Ubbink and Issa, unstructured [10] 0.0397 Present Crank-Nicolson scheme, quadrilaterals 0.0182 Present Crank-Nicolson, triangles 0.0512 Present explicit scheme, quadrilaterals 0.0311 Present explicit scheme, triangles 0.0800 the L 1 -error norm of the final state as defined in [10]. Table I shows the L 1 -error norms as presented in [7,10], as well as those for the current scheme for this example problem. We see that both our implicit and our explicit schemes on the quadrilateral element mesh are comparable to those of Ubbink and Issa's.…”