UBC Theses and Dissertations
Convergence acceleration of flow solvers using modal decomposition schemes Mirshahi, Amirhossein
Convergence acceleration is a crucial tool for enhancing the efficiency and accuracy of numerical algorithms. Although many numerical flow solvers yield accurate solutions, they may take a long time to converge to the desired tolerance. To address this issue, this thesis proposes a convergence acceleration scheme that employs dynamic mode decomposition (DMD) to generate an over-relaxation update for flow solvers. The DMD analysis identifies the dominant solution modes causing the slow convergence of the flow solver and relaxes them towards their steady-state by extrapolating these modes to infinity and constructing a linear combination of extrapolated sums. The thesis also proposes an automation framework that leverages a machine learning pipeline to automate the application of this DMD acceleration scheme. The pipeline evaluates the DMD-generated over-relaxation updates and assesses whether they will result in convergence acceleration or not, thus ensuring a more robust convergence acceleration framework. We demonstrate that our technique accelerates the convergence of finite-volume computations and that it can achieve instantaneous convergence for linear problems and two to five orders of magnitude reduction in residual for laminar and turbulent problems. Also we show that the automation framework can successfully automate this process and eliminate the need for any input or control of the algorithm. We also demonstrate that the automation framework can apply this technique without any user intervention. The proposed convergence acceleration framework is entirely data-driven and can be integrated into a flow solver as a module which only needs a few solution updates as its input. This scheme is particularly useful for researchers who are satisfied with their flow solver's performance but seek to accelerate it without altering their code implementation by adopting more complex time-advance schemes and time stepping methods.
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