Solving a thermal regenerator model using implicit Newton-Krylov methods

In this article we discuss the use of an implicit Newton-Krylov method to s olve a set of partial differential equations (PDEs) representing a physical model of a blast furnace stove. Blast furnace stoves ave thermal regenerat ors used to heat the air injected into the blast furnace, providing the hea t to chemically reduce iron oxides to iron. The stoves are modeled using a set of PDEs that describe the heatflow in the system. The model is used as a part of a predictive controller that minimizes the fuel gas consumption d uring the heating cycle while maintaining a high enough output air temperat ure in the cooling cycle to drive the chemical reaction in the blast furnac e. The discrete representation of this model is solved with a preconditione d implicit Newton-Krylov technique. This algorithm uses Newton's method, in which the update to the current solution at each stage is computed by solv ing a linear system. This linear system is obtained by linearizing the disc rete approximation to the PDEs, using a numerical approximation for the Jac obian of the discretized system. This linear system is then solved for the needed update using a preconditioned Krylov subspace projection method.