Fully-conservative contact-capturing schemes for multi-material advection

• Published in: Journal of computational physics Vol. 398; p. 108809
• Main Author: Williams, R.J.R.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.12.2019; Elsevier Science Ltd
• Subjects: Advection; Computational physics; Contact pressure; Euler-Lagrange equation; Finite element method; Material properties; Advection
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.07.008

•Fully conservative, contact-maintaining schemes for multi-material advection.•Maintains uniform pressure and temperature at contacts between unlike materials.•Flexible approach, based on requiring thermodynamic consistency in reconstruction.•Demonstrated in both high-resolution Godunov and staggered grid codes. We present a number of fully-conservative, four-equation, multicomponent reconstruction schemes for the Euler equations, which have been designed to maintain both constant pressure and temperature at isothermal contact discontinuities, as is required by thermodynamic consistency. The schemes we discuss have been implemented in AWE's staggered-mesh detailed turbulence modelling code TURMOIL and also in a finite-volume Riemann-solver based code. We show results for a problem where material properties with a high contrast in adiabatic index and material specific heat lead to substantial pressure and temperature perturbations for a simple mass fraction model. The improved schemes maintain the isobaric and isothermal nature of the initial condition to numerical precision.