An optimal constrained approach for divergence-free velocity interpolation and multilevel VOF method

• Published in: Computers & fluids Vol. 47; no. 1; pp. 101 - 114
• Main Authors: Cervone, Antonio, Manservisi, Sandro, Scardovelli, Ruben
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2011; Elsevier
• Subjects: Computational fluid dynamics; Computational methods in fluid dynamics; Constraints; Divergence-free velocity projection; Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Interface reconstruction and advection; Interpolation; Mathematical analysis; Multilevel; Multilevel VOF method; Multiphase and particle-laden flows; Nonhomogeneous flows; Optimal interpolation; Optimization; Phases; Physics; Multilevel VOF method; Interface reconstruction and advection; Optimal interpolation; Divergence-free velocity projection; Interfaces; Multiple deck method; Computational fluid dynamics; Two-phase flow; Refinement method; Digital simulation; Modelling; Velocity distribution; Immiscible fluid; Mesh generation
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2011.02.014

The use of mesh refinement techniques is becoming more and more popular in computational fluid dynamics, from multilevel approaches to adaptive mesh refinement. In this paper we present a new method to interpolate the coarse velocity field which is based on an optimal approach and is characterized by a constrained minimization of an objective functional. The functional contains the sum of the square difference between the velocity components and their target average value subject to a number of divergence-free constraints. In this work we describe this approach in two- and three-dimensional geometries with different discrete velocity field configurations. This technique is applied to a multilevel Volume-of-Fluid (VOF) method where the volume fraction function is used to reconstruct and advect the interface between two immiscible phases. The coarse velocity field is interpolated to a fixed fine grid with the optimal approach over a given number of refinement levels. The results of several kinematic tests are presented, where the mass and geometrical errors are compared with those obtained with refined velocity fields interpolated with a simple midpoint rule.