Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
A continuum method for modeling surface tension
Journal of Computational Physics
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
Modelling merging and fragmentation in multiphase flows with SURFER
Journal of Computational Physics
Temporal evolution of periodic disturbances in two-layer Couette flow
Journal of Computational Physics
Reconstructing volume tracking
Journal of Computational Physics
Journal of Computational Physics
Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method
Journal of Computational Physics
A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations
Journal of Computational Physics
Accurate representation of surface tension using the level contour reconstruction method
Journal of Computational Physics
Three-dimensional numerical investigation of a droplet impinging normally onto a wall film
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
A Volume Tracking (VT) and a Front Tracking (FT) algorithm are implemented and compared for locating the interface between two immiscible, incompressible, Newtonian fluids in a tube with a periodically varying, circular cross-section. Initially, the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube (core fluid) and the other one surrounds it (annular fluid). A constant pressure gradient sets them in motion. With both VT and FT, a boundary-fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry. The surface tension force is approximated using the continuous surface force method. All terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one-sided forward finite differences in time. In each time step, the incompressibility condition is enforced by a transformed Poisson equation, which is linear in pressure. This equation is solved by either direct LU decomposition or a Multigrid iterative solver. When the two fluids have the same density, the former method is about 3.5 times faster, but when they do not, the Multigrid solver is as much as 10 times faster than the LU decomposition. When the interface does not break and the Reynolds number remains small, the accuracy and rates of convergence of VT and FT are comparable. The well-known failure of centered finite differences arises as the Reynolds number increases and leads to non-physical oscillations in the interface and failure of both methods to converge with mesh refinement. These problems are resolved and computations with Reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third-order upwind differences using Lagrangian Polynomials. When the volume of the core fluid or the Weber number decrease, increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid, the FT method converges faster with mesh refinement than the VT method and upwinding may be required. Finally, examining the generation of spurious currents around a stationary ''bubble'' in the tube for Ohnesorge numbers between 0.1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when VT is applied, whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when FT is applied.