CONSERVATIVE HIGH-ORDER TIME INTEGRATION FOR LAGRANGIAN HYDRODYNAMICS

This work develops novel time integration methods for the compressible Euler equations in the Lagrangian frame that are of arbitrary high order and exactly preserve the mass, momentum, and total energy of the system. The equations are considered in nonconservative form, that is, common for staggered grid hydrodynamics (SGH) methods; namely, the evolved quantities are mass, momentum, and internal energy. A general family of time integration schemes is formulated, and practical pairs for orders three and four are derived. Numerical results on standard hydrodynamics benchmarks confirm the high-order convergence on smooth problems and the exact numerical preservation of all physically conserved quantities.

Automated summary

This study introduces novel high-order time integration methods for solving the compressible Euler equations in the Lagrangian frame, which accurately preserve the mass, momentum, and total energy of the system. Numerical results on standard hydrodynamics benchmarks demonstrate high-order convergence on smooth problems and exact numerical preservation of all physically conserved quantities.