Modelling of fluid–solid interactions using an adaptive mesh fluid model coupled with a combined finite–discrete element model
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Fluid–structure interactions are modelled by coupling the finite element fluid/ocean model ‘Fluidity-ICOM’ with a combined finite–discrete element solid model ‘Y3D’. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid’s equations. Importantly, the proposed approach ensures that Newton’s third law is satisfied at the discrete level. This is done by first computing the action–reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.
KeywordsFluid–structure interactions Finite element method Discrete force conservation Supermesh Falling sphere Vortex-induced vibrations Deformable fibres
The authors wish to acknowledge support from EPSRC (under projects EP/I00405X/1 and EP/H030123/1) and NERC (under grant NE/F012594/1), as well as the Grantham Institute for Climate Change and the High Performance Computing Service at Imperial College London. A.V. is supported by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement PIEF-GA-2010-272437, and she is also grateful to the Belgian Vocatio Foundation. P.E.F.’s work was supported by a Center of Excellence grant from the Norwegian Research Council to the Center for Biomedical Computing at Simula Research Laboratory. The content of this paper reflects only the authors views and not those of the European Commission.
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