A modified finite element method for solving the timedependent, incompressible NavierStokes equations. I Theory
Abstract
The present investigation is concerned with a numerical method which has been developed for solving the timedependent, incompressible NavierStokes equations (or variants, such as the Boussinesq equations or the anelastic equations) and the advectiondiffusion equation in two and three dimensions. The technique was originally derived via the conventional Galerkin finite element method. In the current investigation, attention is given to two ensuing simplifying approximations which generate a scheme that is probably better described as a blend of finite elements and finite differences, i.e., an 'isoparametric element, finite difference method'. The governing equations and basic spatial discretization are considered along with a onepoint quadrature and its effects, and time integration.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 June 1984
 DOI:
 10.1002/fld.1650040608
 Bibcode:
 1984IJNMF...4..557G
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 Flow Equations;
 Incompressible Flow;
 NavierStokes Equation;
 Advection;
 Diffusion Theory;
 Gravity Waves;
 Quadratures;
 Tensors;
 Time Dependence;
 Fluid Mechanics and Heat Transfer