FULLY COUPLED FINITE-VOLUME SOLUTIONS OF THE INCOMPRESSIBLE NAVIER-STOKES AND ENERGY EQUATIONS USING AN INEXACT NEWTON METHOD

An inexact Newton method is used to solve the steady, incompressible N avier-Stokes and energy equations. Finite volume differencing is emplo yed on a staggered grid using the power law scheme of Patankar. Natura l convection in an enclosed cavity is studied as the model problem. Tw o conjugate-gradient-like algorithms based upon the Lanczos biorthogon alization procedure are used to solve the linear systems arising on ea ch Newton iteration, The first conjugate-gradient-like algorithm is th e transpose-free quasi-minimal residual algorithm (TFQMR) and the seco nd is the conjugate gradients squared algorithm (CGS). Incomplete lowe r-upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton-TFQMR algorithm is studi ed with regard to different choices for the TFQMR convergence criteria and the amount of fill-in allowed in the ILU factorization. Performan ce data are compared with results using the Newton-CGS algorithm and p revious results using LINPACK banded Gaussian elimination (direct-Newt on). The inexact Newton algorithms were found to be CPU competetive wi th the direct-Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton-CGS outperformed Newton-TFQMR w ith regard to CPU time but was less robust because of the sometimes er ratic CGS convergence behaviour.