COMPARISON OF NEWTON AND QUASI-NEWTON METHOD SOLVERS FOR THE NAVIER-STOKES EQUATIONS

The results of a computational evaluation of several Newton's and quas i-Newton's method solvers are discussed and analyzed. Computer time an d memory requirements for iterating a solution to the steady state are recorded for each method. Roe's flux-difference splitting together wi th the Spekreijse/Van Albada continuous limiter is used for the spatia l discretization. Sparse matrix inversions are performed using a modif ied version of the Boeing real sparse library routines and the conjuga te gradient squared algorithm. The methods are applied to exact and ap proximate Newton's method Jacobian systems for flat plate and flat-pla te/wedge-type geometries. Results indicate that the quasi-Newton's met hod solvers do not exhibit quadratic convergence, but can be more effi cient than the exact Newton's method in select cases.