Fully implicit solutions of the benchmark backward facing step problem using finite element discretization and inexact Newton`s method

Conference · Thu Dec 31 04:00:00 EST 1992

OSTI ID:10117866

McHugh, P R; Knoll, D A

A fully implicit solution algorithm based on Newton`s method is used to solve the steady, incompressible Navier-Stokes and energy equations. An efficiently evaluated numerical Jacobian is used to simplify implementation, and mesh sequencing is used to increase the radius of convergence of the algorithm. We employ finite volume discretization using the power law scheme of Patankar to solve the benchmark backward facing step problem defined by the ASME K-12 Aerospace Heat Transfer Committee. LINPACK banded Gaussian elimination and the preconditioned transpose-free quasi-minimal residual (TFQMR) algorithm of Freund are studied as possible linear equation solvers. Implementation of the preconditioned TFQMR algorithm requires use of the switched evolution relaxation algorithm of Mulder and Van Leer to ensure convergence. The preconditioned TFQMR algorithm is more memory efficient than the direct solver, but our implementation is not as CPU efficient. Results show that for the level of grid refinement used, power law differencing was not adequate to yield the desired accuracy for this problem.

• Research Organization: EG and G Idaho, Inc., Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC07-76ID01570
• OSTI ID: 10117866
• Report Number(s): EGG-M--92411; CONF-921110--45; ON: DE93005246
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400
665000
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALGORITHMS
BENCHMARKS
CONVERGENCE
FINITE ELEMENT METHOD
HEAT TRANSFER AND FLUID FLOW
INCOMPRESSIBLE FLOW
NAVIER-STOKES EQUATIONS
NEWTON METHOD
NUMERICAL SOLUTION
PHYSICS OF CONDENSED MATTER