Convergence acceleration for the steady-state Euler equations |
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Authors: | Henrik Brandé n Sverker Holmgren |
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Affiliation: | Department of Scientific Computing, Information Technology, Uppsala University, Box 337, Uppsala S-751 05, Sweden |
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Abstract: | 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 that the time step is not limited by a CFL-criterion. 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. |
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Keywords: | Convergence acceleration Semicirculant approximations Euler equations |
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