Reduced Order Modelling for Dispersive and Nonlinear Water Wave Modelling

This abstract describes our recent work on employing reduced-order modelling (ROM) to solvefully nonlinear potential flow equations (FNPF) to achieve faster turn-around time than a fullorder model (FOM) based on the spectral element method (SEM). We propose a PODGalerkin based model-order reduction approach to reduce the cost of the solve step in theLaplace problem. If repeated simulations are needed for applications, e.g. in optimizationloops with varying parameters, it may become prohibitively expensive to run many FOM simulations in practical times. Reduced-order modelling techniques were introduced to eliminatethe time-consuming behaviour of high-dimensional numerical methods and reduce the loadon computational resources without compromising overall accuracy. The proper orthogonaldecomposition (POD) method is one of the most effective snapshot-based reduced-order modelling techniques and is considered in this work. The basic idea of using POD is to generatea low-dimensional model with few degrees of freedom using the most dominant features of thesystem, thereby significantly reducing the computational time and cost.