TY - JOUR
T1 - An effective implementation of surface tension using the marker and cell method for axisymmetric and planar flows
AU - Mangiavacchi, N.
AU - Castelo, A.
AU - Tomé, M.F.
AU - Cuminato, J.A.
AU - de Oliveira, M.L.B.
AU - McKee, S.
PY - 2005
Y1 - 2005
N2 - This work presents a method for simulating axisymmetric and planar free-surface flows dominated by surface tension forces. The surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is evaluated by fitting a least squares curve to the free surface using the tracking markers in the cell and in its close neighbors. To avoid short wavelength perturbations on the free surface, a mass-conserving local four-point stencil filter is employed. This filter is an extension of the trapezoidal subgrid undulations removal (TSUR) method. The TSUR technique consists of modifying the positions of two ''internal' markers of the four-point stencil in such a way that the surface length and the curvature are minimized, while still preserving the volume. The computation of the curvature is modified at cells adjacent to solid boundaries in order to apply contact angle boundary conditions. To identify neighboring cells efficiently, an implementation is effected through a dual representation of the cell data: in addition to a matrix representation, a list structure is also employed which permits the representation of specific groups of cells and associated data. This technique was implemented in the GENSMAC code, and it has been proved to be robust. The code is shown to produce accurate results when compared with exact solutions of selected fluid dynamical problems involving surface tension. Additionally, it is demonstrated that the method is applicable to complex free-surface flows, such as containers filling, splashing drops, and bursting bubbles.
AB - This work presents a method for simulating axisymmetric and planar free-surface flows dominated by surface tension forces. The surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is evaluated by fitting a least squares curve to the free surface using the tracking markers in the cell and in its close neighbors. To avoid short wavelength perturbations on the free surface, a mass-conserving local four-point stencil filter is employed. This filter is an extension of the trapezoidal subgrid undulations removal (TSUR) method. The TSUR technique consists of modifying the positions of two ''internal' markers of the four-point stencil in such a way that the surface length and the curvature are minimized, while still preserving the volume. The computation of the curvature is modified at cells adjacent to solid boundaries in order to apply contact angle boundary conditions. To identify neighboring cells efficiently, an implementation is effected through a dual representation of the cell data: in addition to a matrix representation, a list structure is also employed which permits the representation of specific groups of cells and associated data. This technique was implemented in the GENSMAC code, and it has been proved to be robust. The code is shown to produce accurate results when compared with exact solutions of selected fluid dynamical problems involving surface tension. Additionally, it is demonstrated that the method is applicable to complex free-surface flows, such as containers filling, splashing drops, and bursting bubbles.
KW - numerical simulation
KW - free-surface flows
KW - surface tension
KW - axisymmetric flow
KW - 2D flow
KW - numerical mathematics
UR - http://dx.doi.org/10.1137/S1064827503427182
U2 - 10.1137/S1064827503427182
DO - 10.1137/S1064827503427182
M3 - Article
SN - 1064-8275
VL - 26
SP - 1340
EP - 1368
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 4
ER -