Non-reflecting boundary conditions for updated Lagrangian hydrodynamics simulations

Abstract

This paper presents a non-reflecting boundary condition (NRBC) strategy specifically designed for compressible flow simulations within an updated Lagrangian hydrodynamic framework. The method is grounded in the characteristic decomposition of the linearized Euler equations, extending the approach pioneered by Giles (Giles, 1990). By analyzing the local eigenstructure of the system, incoming and outgoing waves are precisely identified at the domain boundaries. This identification enables the selective suppression of incoming waves, effectively preventing unwanted reflections. A key advantage of this NRBC approach is its full compatibility with all standard updated Lagrangian schemes, whether staggered or cell-centered. The practical implementation of the NRBC is discussed in detail. Numerical experiments conducted on one-dimensional and two-dimensional problems demonstrate the method’s effectiveness in absorbing outgoing disturbances, confirming its non-reflecting properties.