Studies of reursive projection methods for convergence acceleration of steady state Calculations

Sammanfattning: this paper we have defined two classes of projectionmethods. RPM(m) and NPGS(m), where RPM(1) is the classicalscheme due to Shroff \&Keller. Following the ideas in Lustet al., we obtain NPGS(m). They refer to RPM(m) as NPJ(m).Experiments were conducted on the Cauchy problem for the1D viscous Burger's equation, to find the steady solution. Theamount of non-linearity and its convergence properties aredetermined by the amount of diffusion in the equation.A detailed analysis, based on a linear problem todetermine the convergence properties of the method is performedin the first part of the thesis. Theoretical estimates andnumerical experiments show good agreement.Basis identification was done via a QR-factorization andthe Arnoldi iteration. For problems of limited size, the lattercould be switched on at an earlier stage, i.e. the enhancedconvergence could compensate for the increased costs associatedwith the method. For weakly non-linear problems the sametechniques could be used as for the linear test problem. It issufficient to determine the vectors that span the dominanteigenspace once. As non-linearity increases, other techniqueshad to be incorporated. The Arnoldi iteration could track themoving eigenspace. To obtain convergence a damping parameterwas introduced in the Newton step, chosen by line search/backtracking algorithm. Convergence was a factor 10 faster than theoriginal solver.In the second part of this thesis, the CFD code NSMB(Navier Stokes Multi Block) was run as a black box solver fromMatlab. To accomplish this, NSMB had to be modified and linkedto Matlab via a mex-interface. RPM+NSMB, was tested on two 2Dtest cases, a supersonic nozzle and a subsonic airfoil. Toincrease robustness of RPM, a scaling of the state vectorvariables was introduced. Parameter variations were conducted.The results for QR concurred well the results obtained forlinear problems in the first part of thesis. QR was foundsuperior in number of function evaluations to reachconvergence. For the investigated flow cases, convergence wasreached up to 5 times faster. For the 2 investigated flowcases, good results were obtained. Convergence was reached upto 5 times faster. We therefore conclude that RPM can be usedas an accelerator in CFD applications.