An Eulerian hybrid WENO centered-difference solver for elastic–plastic solids

We present a finite-difference based solver for hyper-elastic and viscoplastic systems using a hybrid of the weighted essentially non-oscillatory (WENO) schemes combined with explicit centered difference to solve the equations of motion expressed in an Eulerian formulation. By construction our approach minimizes both numerical dissipation errors and the creation of curl-constraint violating errors away from discontinuities while avoiding the calculation of hyperbolic characteristics often needed in general finite-volume schemes. As a result of the latter feature, the formulation allows for a wide range of constitutive relations and only an upper-bound on the speed of sound at each time is required to ensure a stable time step is chosen. Several one and two-dimensional examples are presented using a range of constitutive laws with and without additional plastic modeling. In addition we extend the reflection technique combined with ghost-cells to enforce fixed boundaries with a zero tangential stress condition (i.e. free slip).