A Novel Solver Acceleration Technique Based on Dynamic Mode Decomposition

The speed up of finite-volume solvers for compressible flows is a difficult task. There are several ways to achieve solver speed-up, more or less difficult to implement and more or less suitable for implementation in a parallel, unstructured type of solver. Examples of such techniques are the multi-grid method and implicit residual smoothening. In this article, a solver acceleration technique based on Dynamic Mode Decomposition (DMD) is proposed. The technique does not depend on data or mesh structure and is thus as straightforward to implement in an unstructured parallel code as in a structured sequential code. The main idea behind the proposed method is that one can use the information in flow field modes extracted using the DMD technique to find a correction that will bring the solution closer to a steady state condition, i.e. the method is only applicable to steady-state problems. In the presented work the DMD-based acceleration technique has been implemented in a massively parallel block-structured finite-volume Navier-Stokes solver for compressible flows. The method has been tested on a turbine cascade case with promising results. To the knowledge of the authors, the proposed method is not previously published in the open literature