BILUF: a Preconditioner of Linear Solver in Newton's Method for Solving Steady State Laminar Locally Conical Navier-Stokes Equations. G.U. Aero Report 9321.

Abstract

Linearization of the non-linear system arising from Newton's method in solving steady state laminar locally conical Navier-Stokes equations results in a linear system with a large sparse non-symmetric Jacobian matrix, which will be a block 13-point diagonal stencil since high order spatial discretization scheme and structured grid are used. A new suitable arrangement of the matrix elements makes a certain BILU factorization become a very robust preconditioner in GMRES and CGS solvers. The stucture of the matrix is employed in the procedure of generation of the incomplete lower and upper matrices, which greatly reduces the CPU time. These linear solvers significantly accelerate the convergence of the Newton's solver for the hypersonic viscous flows over a cone at high angle of attack, in which the Osher flux difference splitting high resolution scheme is used for capturing both shock waves and shear layers in the flowfield