SOLVING A THERMAL REGENERATOR MODEL USING IMPLICIT NEWTON-KRYLOV METHODS

Abstract

In this article we discuss the use of an implicit Newton?Krylov method to solve a set of partial differential equations (PDEs) representing a physical model of a blast furnace stove. Blast furnace stoves are thermal regenerators used to heat the air injected into the blast furnace, providing the heat to chemically reduce iron oxides to iron. The stoves are modeled using a set of PDEs that describe the heat flow in the system. The model is used as a part of a predictive controller that minimizes the fuel gas consumption during the heating cycle while maintaining a high enough output air temperature in the cooling cycle to drive the chemical reaction in the blast furnace. The discrete representation of this model is solved witha preconditioned implicit Newton?Krylov technique. This algorithm uses Newton's method, in which 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 PDEs, 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.