Implicit Newton-Krylov methods for modeling blast furnace stoves

Conference · Sun Mar 01 04:00:00 EST 1998

OSTI ID:672211

Howse, J W; Hansen, G A; Cagliostro, D J ^[1]; Muske, K R ^[2]

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1. Los Alamos National Lab., NM (United States). Computational Science Methods Group
2. Villanova Univ., PA (United States). Dept. of Chemical Engineering

In this paper the authors discuss the use of an implicit Newton-Krylov method to solve a set of partial differential equations representing a physical model of a blast furnace stove. The blast furnace stove is an integral part of the iron making process in the steel industry. These stoves are used to heat air which is then used in the blast furnace to chemically reduce iron ore to iron metal. The solution technique used to solve the discrete representations of the model and control PDE`s must be robust to linear systems with disparate eigenvalues, and must converge rapidly without using tuning parameters. The disparity in eigenvalues is created by the different time scales for convection in the gas, and conduction in the brick; combined with a difference between the scaling of the model and control PDE`s. A preconditioned implicit Newton-Krylov solution technique was employed. The procedure employs Newton`s method, where the update to the current solution at each stage is computed by solving a linear system. This linear system is obtained by linearizing the discrete approximation to the PDE`s, using a numerical approximation for the Jacobian of the discretized system. This linear system is then solved for the needed update using a preconditioned Krylov subspace projection method.

• Research Organization: Los Alamos National Lab., Computational Science Methods Group, NM (United States)
• Sponsoring Organization: USDOE Assistant Secretary for Management and Administration, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 672211
• Report Number(s): LA-UR--97-4348; CONF-980610--; ON: DE98004239
• Country of Publication: United States
• Language: English

Related Subjects

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION
AIR HEATERS
BLAST FURNACES
CALCULATION METHODS
HEAT TRANSFER
MATHEMATICAL MODELS
METAL INDUSTRY
NUMERICAL SOLUTION