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Lagrangian formulation for finite element analysis of quasi‐incompressible fluids with reduced mass losses
Author(s) -
Oñate Eugenio,
Franci Alessandro,
Carbonell Josep M.
Publication year - 2014
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3870
Subject(s) - finite element method , discretization , compressibility , mathematics , slosh dynamics , interpolation (computer graphics) , mechanics , pressure correction method , added mass , incompressible flow , flow (mathematics) , mathematical analysis , classical mechanics , geometry , engineering , physics , structural engineering , motion (physics) , vibration , quantum mechanics
SUMMARY We present a Lagrangian formulation for finite element analysis of quasi‐incompressible fluids that has excellent mass preservation features. The success of the formulation lays on a new residual‐based stabilized expression of the mass balance equation obtained using the finite calculus method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities and the pressure. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D quasi‐incompressible free‐surface flow problems using the particle FEM ( www.cimne.com/pfem ). Examples include the sloshing of water in a tank, the collapse of one and two water columns in rectangular and prismatic tanks, and the falling of a water sphere into a cylindrical tank containing water. Copyright © 2014 John Wiley & Sons, Ltd.