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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
