Operator splitting and time accuracy in Lagrange plus remap solution methods

Operator splitting and time accuracy in Lagrange plus remap solution methods for the hydrodynamics equations are investigated. The time accuracy of the common solution approach is shown, both analytically and numerically, to be limited to first order due to operator splitting errors, low-order time integration of the remap terms, and other postulated first-order errors, even if the Lagrange step is second-order accurate in time. Additional numerical studies are used to demonstrate how these errors can be eliminated with an unsplit treatment that solves the remap terms directly. The Discontinuous Remap Method, in which a new mesh is generated during the remap step, also is shown to be first-order accurate in time.