A Localized Accurate VOF Interface Reconstruction Method with Curvature and Corner Definition in Two Dimensions
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Interface reconstruction with VOF (volume of fluids) is an essential requirement in an ALE (Arbitrary Lagrange & Eulerian) simulation. Some historical issues associated with the Youngs method have not been well addressed. One is that the slope estimate is not always accurate, a more serious issue is that interface is discontinuous on cell faces with a given curved interface geometry. Besides, with a VOF method a corner cannot be reconstructed in general. We propose a new VOF approach in order to address these issues. We treat the case of a single material and void, and the partial volumes in mixed cells are exactly given. We assume no node is owned by only mixed elements. This is generally true for a moderate curvature. Exceptions can occur where a corner or curved portion is present and can be dealt with. All the nodes in mixed cells can be coloured with pure elements thus to provide orientation of interface facets. With a given mixed zone in two-dimensions we find its mixed neighbours and there are three partial volumes (or two on boundary) given. A linear facet has two degrees of freedom therefore can be reconstructed with a local optimization with volume matching. Then, in a facet normal coordinate system defined by the above optimization, one can construct a quadratic facet with three degrees of freedom that matches the three partial volumes. This is to say a planar interface geometry can be locally exactly reconstructed away from a corner, and interface curvature can be calculated with volume fractions. The case of a corner can be identified with a sudden slope change and high curvature with noticeable gaps between neighbour facets. Then a local optimization for matching volumes can again be performed and the corner is reconstructed (exactly if volume fractions are consistent with a planar geometry). We have implemented this new algorithm at LLNL. Preliminary tests show that exact planar geometries can be reconstructed, and corners can be accurately defined. In the case of a curved geometry, the gaps between neighbour facets are of high order (hardly visible with even a coarse mesh), this high order of error would help to improve the accuracy of an ALE simulation. If necessary, the gaps between facets can be eliminated by a local modification of a facet that does not affect the accuracy of the proposed algorithm. The proposed algorithm is by nature applicable to an arbitrarily given mesh because the only necessary requirement is a function to accurately compute the partial volume bounded by a facet (linear, corner, circular, or quadratic). We expect a similar approach to also work in threedimensions when an accurate method to compute element partial volumes bounded by a curve or corner is provided.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1592985
- Report Number(s):
- LLNL-TR-801883; 1005423
- Country of Publication:
- United States
- Language:
- English
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