Isogeometric Finite Volume Method for Linear Elasticity

This paper extends a recently developed isogeometric finite volume method by the authors for modeling physical problems using the finite volume method and isogeometric analysis. The concept is extended here to three-dimensional elasticity. A spatial discretization scheme is presented, in which two meshes are considered: a primary mesh and a dual mesh. The primary mesh is used for spatial discretization and geometry representation. It relies on non-uniform rational B-Splines, ensuring compatibility with computer aided design models and enabling high-order, high-continuity approximations of the primary solution field. The dual mesh is employed to define the control volumes where the governing equations are enforced in the form of integral balance equations. An intersection-based approach is adopted to define the location and construction of the control volumes. The proposed formulation guarantees both local and global conservation properties. The method is validated through several benchmark problems in two- and three-dimensional elasticity, demonstrating promising results, even in the presence of complex curved boundaries.