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Core Information
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| Title: |
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 (2008) [1] 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 - 2000. POD models using the L2 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 H1 POD
projector in preference to the L2 POD projector. The POD bases are constructed
by incorporating gradients as well as function values in the H1 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 e ffect 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 H1 norm and increasing the number of snapshots and POD bases.
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| Keywords: |
reduced-order modelling; ocean model; finite element; unstructured adaptive mesh; POD. |
Author Information
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Detailed Scientific Article Information
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Subjects Information
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1. Oceanography
2. Mathematics
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