Relaxation techniques for high-order discretizations of steady compressible inviscid flows
There does not exist a definite best strategy to advance high-order discretizations of inviscid compressible flows to steady state. The need for a wide range of possible time-relaxation strategies is determined by different possible difficulties: stability issues, stiffness of the matrix, memory limitations, ill-conditioning, and slow convergence. We outline the main available methods and identify the kind of problems for which they are more suitable. We extensively describe the idea of the matrix-free Squared Preconditioning and apply it for the first time also to a Newton iteration nonlinearly preconditioned by means of the flow solver. We apply this approach to inviscid flows in order to study the tuning of its many parameters and to assess its potential. © 2010 by F. Iacono, G. May and Z.J. Wang.
