Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes

Authors:
P. Moinier;M. B. Giles
Affiliations:
Computing Laboratory, Numerical Analysis Group, Oxford University, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom;Computing Laboratory, Numerical Analysis Group, Oxford University, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
Venue:
Journal of Computational Physics
Year:
2002

Citing 6
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Abstract

This paper analyses the stability of a discretisation of the Euler equations on 3D unstructured grids using an edge-based data structure, first-order characteristic smoothing, a block-Jacobi preconditioner, and Runge-Kutta timemarching, This is motivated by multigrid Navier-Stokes calculations in which this inviscid discretisation is the dominant component on coarse grids.The analysis uses algebraic stability theory, which allows, at worst, a bounded linear growth in a suitably defined "perturbation energy" provided the range of values of the preconditioned spatial operator lies within the stability region of the Runge-Kutta algorithm. The analysis also includes consideration of the effect of solid wall boundary conditions, and the addition of a low Mach number preconditioner to accelerate compressible flows in which the Mach number is very low in a significant portion of the flow.Numerical results for both inviscid and viscous applications confirm the effectiveness of the numerical algorithm and show that the analysis provides accurate stability bounds.