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Lagrangian finite element analysis applied to viscous free surface fluid flow
Author(s) -
Ramaswamy Balasubramaniam,
Kawahara Mutsuto
Publication year - 1987
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.1650070906
Subject(s) - finite element method , mathematics , discretization , partial differential equation , pressure correction method , free surface , incompressible flow , compressibility , galerkin method , flow (mathematics) , mixed finite element method , fluid dynamics , mathematical analysis , mathematical optimization , mechanics , geometry , physics , thermodynamics
A new Lagrangian finite element formulation is presented for time‐dependent incompressible free surface fluid flow problems described by the Navier‐Stokes equations. The partial differential equations describing the continuum motion of the fluid are discretized using a Galerkin procedure in conjunction with the finite element approximation. Triangular finite elements are used to represent the dependent variables of the problem. An effective time integration procedure is introduced and provides a viable computational method for solving problems with equality of representation of the pressure and velocity fields. Its success has been attributed to the strict enforcement of the continuity constraint at every stage of the iterative process. The capabilities of the analysis procedure and the computer programs are demonstrated through the solution of several problems in viscous free surface fluid flow. Comparisons of results are presented with previous theoretical, numerical and experimental results.