Implicit mixed interpolation finite element algorithm for time dependent viscous flows utilizing a frontal solution technique

Conference · Tue Jan 01 04:00:00 EST 1985

OSTI ID:5207080

Becker, B R; Drake, J B

A finite element algorithm is described implements the Galerkin approximation to the Navier-Stokes 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 nine-node, Lagrangian, isoparametric, quadrilateral element is used to represent the velocity while the pressure uses a four-node, 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 non-linear equations at each time step. Results are given from the calculations of two dimensional, steady-state and time-dependent convection dominated flows of viscous incompressible fluids.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 5207080
• Report Number(s): CONF-850758-2; ON: DE85016357
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
ALGORITHMS
BOUNDARY CONDITIONS
COUETTE FLOW
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
FLOW MODELS
FLUID FLOW
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PRESSURE EFFECTS
TIME DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS
VISCOUS FLOW