Fully implicit solutions of the benchmark backward facing step problem using finite element discretization and inexact Newton's method
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; USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC07-76ID01570
- OSTI ID:
- 6817717
- Report Number(s):
- EGG-M-92411; CONF-921110-45; ON: DE93005246
- Resource Relation:
- Conference: Winter annual meeting of the American Society of Mechanical Engineers (ASME), Anaheim, CA (United States), 8-13 Nov 1992
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
42 ENGINEERING
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
ALGORITHMS
BENCHMARKS
CONVERGENCE
FINITE ELEMENT METHOD
INCOMPRESSIBLE FLOW
NEWTON METHOD
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
ITERATIVE METHODS
MATHEMATICAL LOGIC
PARTIAL DIFFERENTIAL EQUATIONS
665000* - Physics of Condensed Matter- (1992-)
420400 - Engineering- Heat Transfer & Fluid Flow