Pseudospectral element model for free surface viscous flows

Purpose - The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The paper describes the methodology, and gives illustrative results for simple geometries.

Design/methodology/approach - The pseudospectral matrix element method of discretisation is selected as the basis for the CFD technique adopted, because of its high spectral accuracy. It is implemented as a means of solving the Navier-Stokes equations coupled with the modified compressibility method.

Findings - The viscous solver has been validated for the benchmark cases of uniform flow past a cylinder at a Reynolds number of 40, and 2D cavity flows. Results for sloshing of a viscous fluid in a tank have been successfully compared with those from a linearised analytical solution. Application of the method is illustrated by the results for the interaction of an impulsive wave with a surface piercing circular cylinder in a cylindrical tank.

Research limitations/implications - The paper demonstrates the viability of the approach adopted. The limitation of small amplitude waves should be tackled in future work.

Practical implications - The results will have particular significance in the context of validating computations from more complex schemes applicable to arbitrary geometries.

Originality/value - The new methodology and results are of interest to the community of those developing numerical models of flow past marine structures.