Particle finite element method in fluid-mechanics including thermal convection-diffusion

• Published in: Computers & structures Vol. 83; no. 17; pp. 1459 - 1475
• Main Authors: Aubry, R., Idelsohn, S.R., Oñate, E.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier Ltd 01.06.2005; Elsevier Science
• Subjects: Analytical and numerical techniques; Computational techniques; Convection and heat transfer; Coupled thermo-mechanical analysis; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Heat transfer; Incompressible fluid flow; Lagrangian description; Mathematical methods in physics; Particle method; Physics; Rayleigh–Bénard instability with free surface; Thermal convection; Turbulent flows, convection, and heat transfer; Lagrangian description; Coupled thermo-mechanical analysis; Particle method; Thermal convection; Rayleigh–Bénard instability with free surface; Incompressible fluid flow; Thermal diffusion; Heat flow; Boussinesq model; Convection diffusion equation; Free surface; Convection; Finite element method; Fixed point theorem; Modelling; Mesh generation; Surface instability; Fluid mechanics; Rayleigh-Bénard instability with free surface; Lagrangian; Fractional step method; Thermomechanical properties; Incompressible flow; Meshless method; Incompressible fluid; Non linear effect; Viscous fluids; Heat transfer; Viscous flow
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2004.10.021

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.