POD enriched boundary models and their optimal stabilisation
L. Chen, Wouter N. Edeling, Steven J. Hulshoff · International Journal for Numerical Methods in Fluids · 2014
SUMMARY Modes obtained using the Proper Orthogonal Decomposition are used as boundary enrichment functions within a variational multiscale method for the stochastically forced Burgers equation. Initially, large increases in accuracy are obtained using the enrichment functions without stabilisation terms. Then, optimal coefficients for the stabilisation parameter τ of the unresolved scale model are calibrated using a goal‐oriented model‐constrained optimisation technique, resulting in further improvements. As both the determination of the enrichment functions and the optimisation of the coefficients requires high‐accuracy reference data, a scaling procedure is introduced to allow their use over range of conditions. Numerical experiments confirm that the scaling procedure is effective. Copyright © 2014 John Wiley & Sons, Ltd.