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2010 On the second-order accuracy of volume-of-fluid interface reconstruction algorithms: convergence in the max norm
Elbridge Puckett
Commun. Appl. Math. Comput. Sci. 5(1): 99-148 (2010). DOI: 10.2140/camcos.2010.5.99

Abstract

Given a two times differentiable curve in the plane, I prove that — using only the volume fractions associated with the curve — one can construct a piecewise linear approximation that is second-order in the max norm. I derive two parameters that depend only on the grid size and the curvature of the curve, respectively. When the maximum curvature in the 3 by 3 block of cells centered on a cell through which the curve passes is less than the first parameter, the approximation in that cell will be second-order. Conversely, if the grid size in this block is greater than the second parameter, the approximation in the center cell can be less than second-order. Thus, this parameter provides an a priori test for when the interface is under-resolved, so that when the interface reconstruction method is coupled to an adaptive mesh refinement algorithm, this parameter may be used to determine when to locally increase the resolution of the grid.

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Elbridge Puckett. "On the second-order accuracy of volume-of-fluid interface reconstruction algorithms: convergence in the max norm." Commun. Appl. Math. Comput. Sci. 5 (1) 99 - 148, 2010. https://doi.org/10.2140/camcos.2010.5.99

Information

Received: 12 June 2009; Accepted: 1 July 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1277.76063
MathSciNet: MR2600824
Digital Object Identifier: 10.2140/camcos.2010.5.99

Subjects:
Primary: 65M06 , 65M12 , 76-04 , 76M20 , 76M25

Keywords: adaptive mesh refinement , computational fluid dynamics , ELVIRA , front reconstruction , fronts , LVIRA , multiphase systems , piecewise linear interface reconstruction , two-phase flow , underresolved computations , volume-of-fluid

Rights: Copyright © 2010 Mathematical Sciences Publishers

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