High-order cell-centered finite volume method for solid dynamics on unstructured meshes

This paper introduces a high -order finite volume method for solving solid dynamics problems on threedimensional unstructured meshes. The method is based on truncated Taylor series constructed about each control volume face using the least squares method, extending the classical finite volume method to arbitrary interpolation orders. As verification tests, a static analytical example for small deformations, a hyperelastic cantilever beam with large deformations, and a cantilever beam subject to a dynamic load are analyzed. The results provide an optimal set of parameters for the interpolation method and allow a comparison with other classic schemes, yielding to improved results in terms of accuracy and computational cost. The final test consists in the simulation of a compressor reed valve in a dynamic scenario mimicking real-life conditions. Numerical results are compared against experimental data in terms of displacements and velocity; then, a comprehensive physical analysis of stresses, caused by bending and impact of the valve, is carried out. Overall, the method is demonstrated to be accurate and effective in handling shear locking, stress concentrations, and complex geometries and improves the effectiveness of the finite volume method for solving structural problems.