A hybrid dynamic mode decomposition algorithm combining random and sparsity promoting and its application to viscoelastic flow around circular cylinder

Dynamic mode decomposition (DMD) algorithm is widely applied to identify the flow characteristics of fluid dynamic field. However, for high-dimensional viscoelastic fluid systems, DMD might often result in unsatisfactory performance because of its huge computation cost. Therefore, we propose an improved dynamic mode decomposition algorithm, called sparsity promoting randomized dynamic mode decomposition (SP-RDMD). In our method, random projection techniques is firstly used to reduce the computational complexity, and then sparsity promoting is furtherly incorporated to remove the non-critical modes. Then we apply this method to study viscoelastic flow around circular cylinder. The numerical results show that the presented algorithm can effectively identify and extract the low-dimensional dynamic structure of viscoelastic fluid with steady state. Comparing with the traditional DMD, SP-RDMD can not only reconstruct the overall flow pattern of the viscoelastic flow field with fewer modes, but also make the reconstructed viscoelastic flow field show more local details. Moreover, the computational efficiency of SP-RDMD could be improved significantly yet.