Implicit mixed interpolation finite element algorithm for time dependent viscous flows utilizing a frontal solution technique
Abstract
A finite element algorithm is described which implements the Galerkin approximation to the NavierStokes equations and incorporates five predominate features. Although none of these five features is unique to this algorithm, their orchestration, as described in this paper, results in an algorithm which is not only easy to implement but also stable, accurate, and robust, as well as computationally efficient. The zero stress natural boundary condition is implemented which permits calculation of the outflow velocity distribution. A ninenode, Lagrangian, isoparametric, quadrilateral element is used to represent the velocity while the pressure uses a fournode, Lagrangian, superparametric element coincident with the velocity element. The easily implemented, computationally efficient frontal solution technique is used to assemble the element coefficient matrices, impose the boundary conditions, and solve the resulting linear system of equations. An implicit backward Euler time integration rule provides a very stable solution method for time dependent problems. A Picard scheme with a relatively large radius of convergence is used for iteration of the nonlinear equations at each time step. Results are given from the calculations of two dimensional, steadystate and timedependent convection dominated flows of viscous incompressible fluids.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1985
 Bibcode:
 1985STIN...8617669B
 Keywords:

 Algorithms;
 Couette Flow;
 Differential Equations;
 Finite Element Method;
 Flow Equations;
 Interpolation;
 NavierStokes Equation;
 Time Dependence;
 Viscous Flow;
 Computation;
 Incompressible Fluids;
 Multiphase Flow;
 Problem Solving;
 Fluid Mechanics and Heat Transfer