Technical Report 2000-035

Convergence acceleration for the steady state Euler equations

Henrik Brandén and Sverker Holmgren

December 2000


We consider the iterative solution of systems of equations arising from discretizations of the non-linear Euler equations governing compressible flow. The differential equation is discretized on a structured grid, and the steady state solution is computed by a time-marching method.

A convergence acceleration technique based on semicirculant approximations of the difference operator or the Jacobian is used. Implementation issues and variants of the scheme allowing for a reduction of the arithmetic complexity and memory requirement are discussed. The technique can be combined with a variety of iterative solvers, but we focus on non-linear explicit Runge-Kutta time-integration schemes. The results show that the single-stage forward Euler method can be used, and the time step is not limited by a CFL-criterion. Instead it can be chosen as a constant, independent of the number of grid points. This results in that the arithmetic work required for computing the solution is equivalent to the work required for a fixed number of residual evaluations.

Two major advantages of the semicirculant convergence acceleration technique is that it contains few tunable parameters, and that it is robust with respect to the amount of artificial viscosity used in the discretization.

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