Abstract
Reconstructing the interface within a cell, based on volume fraction and normal direction, is a key part of multiphase flow solvers which make use of piecewise linear interface calculation (PLIC) such as the Coupled Level Set Volume of Fluid (CLSVOF) method. In this paper, we present an iterative method for interface reconstruction (IR) in general convex cells based on tetrahedral decomposition. By splitting the cell into tetrahedra prior to IR the volume of the truncated polyhedron can be calculated much more rapidly than using existing clipping and capping methods. In addition the root finding algorithm is designed to take advantage of the nature of the relationship between volume fraction and interface position by using a combination of Newton's and Muller's methods. In stand-alone tests of the IR algorithm on single cells with up to 20 vertices the proposed method was found to be 2 times faster than an implementation of an existing analytical method, while being easy to implement. It was also found to be 3.4–11.8 times faster than existing iterative methods using clipping and capping and combined with Brent's root finding method. Tests were then carried out of the IR method as part of a CLSVOF solver. For a sphere deformed by a prescribed velocity field the proposed method was found to be up to 33% faster than existing iterative methods. For simulations including the solution of the velocity field the maximum speed up was found to be approximately 52% for a case where 12% of cells lie on the interface. Analysis of the full simulation CPU time budget also indicates that while the proposed method has produced a considerable speed-up, further gains due to increasing the efficiency of the IR method are likely to be small as the IR step now represents only a small proportion of the run time.
Highlights
Besides geometric Volume of Fluid (VOF) [1,2], many high-order methods based on Piecewise linear interface calculation (PLIC)-VOF formulation have been implemented such as Moment of Fluid (MOF) [3], MOF coupled with Level Set [4] and Coupled Level Set and Volume
A significant performance gain over previous, widely used methods for interface reconstruction (IR) has been achieved by decomposing the cell to tetrahedra prior to the IR step which allows for efficient calculation of the truncated polyhedron volume at each iteration and by using a root-finding method designed purposely for the characteristics of the IR problem
A number of numerical tests have been provided to assess the numerical performance of different IR methods, i.e. the proposed one, Clipcap with Brent’s and an analytical method
Summary
Among the most popular and widely used multiphase flow simulation methods are those based on a Volume of Fluid (VOF) formulation. We propose an iterative method for interface reconstruction in a PLIC formulation that performs comparably with analytical methods and is simpler in implementation. As the IR procedure is never used by itself, the focus of the present paper is a comparison of IR methods both in isolation and in a multiphase solver to assess the real advantage of using higher efficiency methods and the potential for further improvement For this purpose the IR methods are implemented in a Coupled Level Set Volume of Fluid solver [8]; (1) without momentum solver for the deformation of a sphere and (2) with momentum solver for drop impingement cases and rivulet flow. The performance of the proposed method in a multiphase solver, implemented in the OpenFOAM CFD suite [17], is assessed in Section 5 in comparison to results employing an existing iterative method for IR
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