A vertex centred Finite Volume Jameson–Schmidt–Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics

A vertex centred Finite Volume algorithm is presented for the numerical simulation of fast transient dynamics problems involving large deformations. A mixed formulation based upon the use of the linear momentum, the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two-dimensional and three-dimensional computations, respectively. The scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the Jameson–Schmidt–Turkel (JST) artificial dissipation term. The discretisation in time is performed by using a Total Variational Diminishing (TVD) two-stage Runge–Kutta time integrator. The JST algorithm is adapted in order to ensure the preservation of linear and angular momenta. The framework results in a low order computationally efficient solver for solid dynamics, which proves to be very competitive in nearly incompressible scenarios and bending dominated applications.