Development of robust and efficient algorithms for solving aerodynamic flows

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The proposed research focuses upon improving computational fluid dynamics (CFD) algorithms for use in modelling turbulent aerodynamic flows. Numerical analysis tools based upon CFD have become a fundamental part of design in aerospace and automotive industries. Obtaining accurate modelling solutions in minimal time while reducing computational cost is critical to CFD tool success within industry. Current CFD tools typically require a substantial amount of specialized knowledge beyond the physical problem at hand which may hinder the tool's effectiveness. This research will seek to develop methods for reducing the tool-specific knowledge requirement while producing CFD algorithms which are as fast as possible for modelling turbulent flow. The following approach is proposed. Beginning with a multigrid-based solver, parameters which affect solver performance may be optimized based upon Fourier analysis to maximize propagation and damping of error modes while maximizing the accuracy of the solution. Solver parameter selection may thus be automated based upon local flow conditions and mesh geometry. To reduce the range of optimal parameter combinations, it is necessary to investigate the best combination of preconditioning and coarsening techniques to reduce discrete numerical stiffness and disparity in propagative speeds. While Fourier analysis provides an estimate of an algorithm's performance and stability it can also be misleading with respect to numerical stability limits. An investigation of numerical stability using algebraic stability theory (or energy methods) may yield optimal parameters with better and more consistent performance. Together these investigations should improve the CFD community's understanding of numerical performance, and lead to better implemented solvers where the user need only focus on the physics of the problem being modelled.