In computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction, moving-mesh methods enable mesh-resolution control near the interface and consequently high-resolution representation of the boundary layers. Good moving-mesh methods require good mesh moving methods. We introduce a low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state (ZSS). The method has been developed targeting isogeometric discretization but is also applicable to finite element discretization. With the large-deformation mechanics equations, we can expect to have a unique mesh associated with each step of the boundary or interface motion. With the fibers placed in multiple directions, we stiffen the element in those directions for the purpose of reducing the distortion during the mesh deformation. We optimize the ZSS by seeking orthogonality of the parametric directions, by mesh relaxation, and by making the ZSS time-dependent as needed. We present 2D and 3D test computations with isogeometric discretization. The computations show that the mesh moving method introduced performs well.
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