| Summary: | One of the key research topics in the computational fluid dynamics (CFD) community is to improve the convergence speed of time-stepping schemes in steady-state finite volume codes. This thesis focuses on the improvements of an implicit time stepping scheme suitable for the fast convergence of a residual which is discretised for a second order accuracy in space. The optimised implicit scheme replaces an explicit scheme implementation in the Rolls-Royce corporate CFD code Hydra. This replacement of the explicit scheme by an implicit scheme is motivated by Swanson et al. [1], reporting a net computational speedup of the scheme of a factor 4 − 10. The novelties presented in this work build on the implicit Runge-Kutta time stepping scheme described by Rossow [2] and enhanced by Swanson et al. [1, 3] and focus on two key aspects: The optimisation of Runge-Kutta coefficients and adequate implicit preconditioning. With regards to the Runge-Kutta coefficients optimisation, the flow conditions leading to slow convergence are first analysed. Based on this analysis, an optimisation procedure is proposed to find an optimal set of Runge-Kutta coefficients. With regards to the improvement of the implicit preconditioner, most notably a novel design of its viscous components is proposed. This novel design of the viscous preconditioner is shown to enhance the convergence reliability of the code on skewed meshes. Compared to the explicit implementation, the implicit code typically achieves a minimum six-fold speedup in terms of computation time on a well defined set of test cases. Compared to the latest coefficients reported in literature [3], the optimised Runge-Kutta coefficients lead to a speedup of 20% − 38%.
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