Evolving boundary problems for which the deformation of a solid body is driven by fluid dynamics were explored using a deforming mesh method, modified to handle large volume and shape deformations. First, the substantial erosion of a cylinder in cross flow within the subcritical flow regime was simulated, where a resulting terminal form emerged that continued until the cylinder completely vanished; closely matching the findings of a corresponding experiment. The terminal shape of the originally circular cylinder was a rounded wedge, pointed upstream, which had an approximately uniform wall shear stress distribution on its surface. Next, the melting front of ice around a heated cylinder was modelled by simulating the molten ice region and tracking the water-ice interface over time. Heat transfer by conduction was dominant when the ice was near the cylinder, and then natural convection developed and enhanced the melting rate as the molten ice volume increased and vortices formed. Lastly, the morphodynamics of deposited silica in pipe flow was simulated by modelling the transport and deposition of the colloidal sized silica particles from the fluid and raising the silica bed as a function of the deposited particle flux. We found that microscale surface roughness reduced the deposition rate by 20%, and that initial protrusions on the surface would grow faster than their surrounding valleys: in agreement with experimental observations. Smoothing methods were applied for the nodes within the interior mesh to absorb the significant volume change in the computational domain. Similarly, a novel node shuffle algorithm is introduced to preserve the mesh quality of the interface boundary where it significantly transformed shape. This algorithm is both shape and volume preserving such that the mesh quality is retained, whilst not artificially contributing to the interface kinematics. We also discuss the importance of monitoring skewness of the finite volume cells in moving boundary problems, and provide insight for undertaking deforming mesh simulations.