Approximate Jacobians for the Solution of the Euler and Navier-Stokes Equations. G.U. Aero Report 9705

This paper describes a method for efficiently solving the steady-state Euler and Navier-Stokes equations. Robustness is achieved through the use of an upwind TVD scheme for discretising the convective terms. The approximate solution is advanced in time implicitly and the linear system arising at each implicit step is solved using a Conjugate Gradient type method. The main emphasis of this paper is on the use of Jacobian matrices associated with a simpler spatial discretisation. This leads to better conditioned linear systems. The resulting method has lower memory and CPU-time requirements when compared with the one using exact Jacobians