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The paper presents a novel method for numerically modelling fluid-structure interactions. The method consists of solving the fluid-dynamics equations on an extended domain, where the computational mesh covers both fluid and solid structures. The fluid and solid velocities are relaxed to one another through a penalty force. The latter acts on a thin shell surrounding the solid structures. Additionally, the shell is represented on the extended domain by a non-zero shell-concentration field, which is obtained by conservatively mapping the shell mesh onto the extended mesh. The paper outlines the theory underpinning this novel method, referred to as the immersed-shell approach. It also shows how the coupling between a fluid- and a structural-dynamics solver is achieved. At this stage, results are shown for cases of fundamental interest., (© 2015 The Author(s) Published by the Royal Society. All rights reserved.)

Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimization-based approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.