An approximate linearised Riemann solver for the Euler equations for real gases
Journal of Computational Physics
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
Computer Methods in Applied Mechanics and Engineering
A conservative formulation for plasticity
Advances in Applied Mathematics
IMPACT of Computing in Science and Engineering
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations
SIAM Journal on Scientific Computing
Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme
Computers and Structures
Accuracy preserving limiter for the high-order accurate solution of the Euler equations
Journal of Computational Physics
Monoslope and multislope MUSCL methods for unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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A novel computational methodology is presented for the numerical analysis of fast transient dynamics phenomena in large deformations. The new mixed formulation can be written in the form of a system of first order conservation laws, where the linear momentum, the deformation gradient tensor and the total energy of the system are used as main conservation variables, leading to identical convergence patterns for both displacements and stresses. A cell centred Finite Volume Method is utilised to carry out the spatial discretisation. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose approximate solution is derived. A suitable numerical interface flux is evaluated by means of the Rankine-Hugoniot jump conditions. We take advantage of the conservative formulation to introduce a Total Variation Diminishing shock capturing technique to improve dramatically the performance of the algorithm in the vicinity of sharp solution gradients. A series of numerical examples will be presented in order to demonstrate the capabilities of the scheme. The new formulation is proven to be very efficient in nearly incompressible and bending dominated scenarios in comparison with classical finite element displacement-based approaches. The proposed numerical framework provides a good balance between accuracy and speed of computation.