Volume consistency in a staggered grid Lagrangian hydrodynamics scheme

Staggered grid Lagrangian schemes for compressible hydrodynamics involve a choice of how internal energy is advanced in time. The options depend on two ways of defining cell volumes: an indirect one, that guarantees total energy conservation, and a direct one that computes the volume from its definition as a function of the cell vertices. It is shown that the motion of the vertices can be defined so that the two volume definitions are identical. A so modified total energy conserving staggered scheme is applied to the Coggeshall adiabatic compression problem, and now also entropy is basically exactly conserved for each Lagrangian cell, and there is increased accuracy for internal energy. The overall improvement as the grid is refined is less than what might be expected. (C) 2008 Elsevier Inc. All rights reserved.