Closure modeling of low dimensional models using LES analogy

摘要

Proper orthogonal decomposition (POD) is an important reduced order modeling technique in fluid mechanics. The first step in POD is the collection of flow field data at different time steps from Direct numerical simulation. The singular value decomposition extracts the most dominant modes from the collected data. The implementation of Galerkin procedure produces a reduced order model of considered flow field named as POD-ROM (ROM stands for reduced order model). In this paper, We have considered the one-dimensional Burgers equation and developed its reduce order model named as POD-G ROM. Two closure models of POD-ROM have also been implemented on one-dimensional Burgers equation. This work focuses on Smagronisky (POD-S) reduced order model and Dynamic subgrid-scale (POD-D) reduced order model. We have further analyzed the effect of modes on accuracy of solution obtained through POD-D, PODS and POD-G ROMs. It was concluded that accuracy obtained depends upon number of considered modes for all three ROMs (POD-G, POD-S and POD-D). POD-S ROM performs same as POD-D ROM but needs a lot of iteration for Cs optimization. The constraint of Cs estimation through hit and trial is removed in POD-S ROM. This model performs better than POD-S ROM but it is computationally expensive.