Abstract

A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed.

Abstract

We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.

Abstract

We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM) and a lagrangian description. The necessary stabilization for dealing with the incompressibility condition is introduced via the so called finite calculus (FIC) method. Both a quasi-implicit algorithm and a fractional step scheme are described. Examples of application of the lagrangian flow description are presented.