A POD reduced order unstructured mesh ocean modelling method for moderate Reynolds number flows

Abstract

Herein a new approach to enhance the accuracy of a novel Proper Orthogonal Decomposition (POD) model applied to moderate Reynolds number flows (of the type typically encountered in ocean models) is presented. This approach develops the POD model of Fang et al. [Fang, F., Pain, C.C., Navon, I.M., Piggott, M.D., Gorman, G.J., Allison, P., Goddard, A.J.H., 2008. Reduced-order modelling of an adaptive mesh ocean model. International Journal for Numerical Methods in Fluids. doi:10.1002/fld.1841] used in conjunction with the Imperial College Ocean Model (ICOM), an adaptive, non-hydrostatic finite element model. Both the velocity and vorticity results of the POD reduced order model (ROM) exhibit an overall good agreement with those obtained from the full model. The accuracy of the POD-Galerkin model with the use of adaptive meshes is first evaluated using the Munk gyre flow test case with Reynolds numbers ranging between 400 and 2000. POD models using the L 2 norm become oscillatory when the Reynolds number exceeds Re = 400 . This is because the low-order truncation of the POD basis inhibits generally all the transfers between the large and the small (unresolved) scales of the fluid flow. Accuracy is improved by using the H 1 POD projector in preference to the L 2 POD projector. The POD bases are constructed by incorporating gradients as well as function values in the H 1 Sobolev norm. The accuracy of numerical results is further enhanced by increasing the number of snapshots and POD bases. Error estimation was used to assess the effect of truncation (involved in the POD-Galerkin approach) when adaptive meshes are used in conjunction with POD/ROM. The RMSE of velocity results between the full model and POD-Galerkin model is reduced by as much as 50% by using the H 1 norm and increasing the number of snapshots and POD bases.