A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

Abstract

SUMMARYA new interface reconstruction method in 3D is presented. The method involves a conservative levelcontour reconstruction coupled to a cubic-Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second-order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required.

A new volume of fluid method in three dimensions—Part I: Multidimensional advection method with face‐matched flux polyhedra

“…This improvement was found not only in the rotation test but also in the test described below. Similar results to those of Table II are presented in Table III using, instead of Youngs' method, the CLC-CBIR reconstruction method proposed in [14], for which a second-order accuracy is achieved. Note that the use of a more accurate reconstruction method makes the difference between the RK-3D and the FMFPA-3D advection methods higher (around 30% for all grids).…”

“…The integral in Equation (2) represents the net VOF advected out of the cell V F T and will be solved geometrically using the face-matched flux polyhedron advection (FMFPA-3D) method proposed in this work, which is described below. Before beginning the description of the proposed advection method, it should be mentioned that, before applying the advection step, the interface will be assumed to have been reconstructed in the previous time step using a PLIC method (such as that proposed in the companion paper [14]), in which the interface is reconstructed in each cell as a plane n·x+C = 0, where n points to the reference fluid. Since the aim of this paper is to assess the proposed advection method, widely used methods, for which many results are available in the literature, will be used to determine the vector normal to the interface, n, and constant C. Thus, unless otherwise stated, n will be obtained from the gradient of the volume fraction function, ∇F, using the method of Youngs [15] (see also [4,16]), and the constant C will be determined from the value of F in the cell and enforcement of local volume conservation using the analytical method of Scardovelli and Zaleski [17] (alternatively, an iterative method, such as Brent's method [18], could also be employed).…”

“…It should be taken into account that, when the CLC-CBIR method is used, the contribution of the reconstruction step to the error E is reduced. A more detailed analysis of the use of the CLC-CBIR reconstruction method in combination with the proposed FMFPA-3D advection method is discussed in the companion paper [14]. Figure 9 shows a comparison between the flux polyhedra constructed using our extension to 3D of the Rider and Kothe [2] method and the face-matched flux polyhedra proposed in this work (Figures 9(a) and (b), respectively).…”

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

“…The 2D advection method was generalized to 3D in [101], the socalled face-matched flux polyhedra, with a NS solver that also accounts for surface tension effects. The spline-based reconstruction is extended to 3D as a piecewise-planar reconstruction with a cubic-Bézier interpolation [142].…”

Analytical and geometrical tools for 3D volume of fluid methods in general grids

“…Numerous successful implementations of high-order PLIC-VOF methods have been developed in two dimensions (2D) during the last two decades (see for example the reviews of Scardovelli and Zaleski [14] or Rider and Kothe [13] and the references therein). However, the great complexity of the geometrical operations involved in these methods makes their extension to three dimensions (3D) relatively difficult (successful implementations of high-order PLIC-VOF methods in 3D can be found in [2,4,5,[8][9][10]12]). …”