A multiphase Lagrangian discontinuous Galerkin hydrodynamic method for high-explosive detonation physics

Abstract

We present a new multidimensional multiphase Lagrangian discontinuous Galerkin (DG) hydrodynamic method that supports programmed burn and reactive burn high-explosive (HE) detonation models. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. The HE reaction mass fraction is represented using a nodal quantity. A new limiting approach is presented along with new special limiting conditions for the reactive burn model. The HE models are applied to individual quadrature points in the DG elements to better resolve the physics with the modal method. In the programmed burn model, this means that reaction times are calculated for each point separately. The Scaled Unified Reactive Front (SURF) reactive burn model uses a lead shock pressure to determine the reaction rate at the quadrature points, with a new lead shock pressure detector that works with the Taylor series polynomials. The temporal evolution of the governing equations is achieved with the total variation diminishing Runge–Kutta (TVD RK) time integration method. The robustness of the new limiting approach is tested using 1D and 2D strong shock gamma-law gas problems. The accuracy of the point-wise programmed burn model is tested using a 1D gamma-law gas verification problem and a 2D radial problem. The implementation of the SURF reactive burn model within the DG method is tested using a 1D shock-to-detonation problem simulating the behavior of PBX-9501 and a 2D confined slab problem simulating the behavior of PBX-9502, both represented by the Davis equations of state with a multiphase modeling method. All 2D results use quadratic elements, which have faces that can bend.

Keywords

• Lagrangian
• Hydrodynamics
• Discontinuous Galerkin
• High-explosive
• Programmed burn
• Reactive burn