Surface Tension Implementation for Gensmac2d

Abstract

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension

A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces

“…Surface and interfacial tension effects are incorporated using an approach similar to the one described in [4] for the two-dimensional case. The computation of the surface and interfacial tension is performed at two levels: first at the sub-grid level, where small undulations in the fronts (free surface and interfaces) are eliminated, and second at cell level, where the curvature at each surface or interface cell is approximated.…”

“…We developed a filter called TSUR-3D (TSUR: Trapezoidal Sub-grid Undulations Removal) which is based on the TSUR filter presented in [4] for the two-dimensional case. The TSUR-3D is applied to the unstructured grid, represented by a ''half-edge'' data structure [14].…”

Local volume‐conserving free surface smoothing

“…The vertex balance procedure is applied to each vertex of the surface in order to move it to a new position on a line passing through p, where p is the average (9), with direction n given by (10). The vertices are displaced in such a way that a local volume is preserved.…”

“…In order to handle free surfaces in 2D, axisymmetric, and 3D domains, we developed three different versions of TSUR. The two-dimensional and axisymmetric versions have been incorporated into the GENSMAC2D code [10] whereas the three-dimensional version is in GENSMAC3D [11]. The GENSMAC codes [12][13][14] have made use of TSUR for several years, but an unified and detailed description of the geometrical and mathematical constructions employed, jointly with the numerical tests asserting the effectiveness of the technique, have not been published.…”

Desenvolvimento de um método numérico implícito para a simulação de escoamentos viscoelásticos com superfícies livres

“…Isto tem se dado, a grosso modo, em duas linhas: xxiii xxiv PREFÁCIO Na primeira, com uma maior quantidade de trabalhos, vemos a adaptação desta técnica para problemas de natureza parecida, que mantêm o cerne do método original e o ampliam de forma que seja possível lidar com problemas cada vez mais complexos. Nesta linha podemos citar, entre outros, [CF99] (por considerar tensão super…cial), [TM00] (por considerar escoamentos com simetria radial), [TM01] (por ampliar as técnicas 2D ao caso 3D), [FR01] (por tratar de escoamentos em regime turbulento) e [SO02] (por tratar de escoamentos multifásicos). Ainda podemos mencionar [TM96], [TM02A], [TM02B], [GF03], [DO03], [GR03], [SL05], [PL06] e [SV07], que ampliaram o GENSMAC para a simulação numérica de escoamentos não-newtonianos regidos por diversas equações constitutivas.…”