  We present the second-order multidimensional Staggered Grid Hydrodynamics
Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD
scheme is based on the staggered finite element discretizations as in [Dobrev
et al., SISC, 2012]. However, the advantage of the residual formulation over
classical FEM approaches consists in the natural mass matrix diagonalization
which allows one to avoid the solution of the linear system with the global
sparse mass matrix while retaining the desired order of accuracy. This is
achieved by using Bernstein polynomials as finite element shape functions and
coupling the space discretization with the deferred correction type
timestepping method. Moreover, it can be shown that for the Lagrangian
formulation written in non-conservative form, our residual distribution scheme
ensures the exact conservation of the mass, momentum and total energy. In this
paper we also discuss construction of numerical viscosity approximations for
the SGH RD scheme allowing to reduce the dissipation of the numerical solution.
Thanks to the generic formulation of the staggered grid residual distribution
scheme, it can be directly applied to both single- and multimaterial and
multiphase models. Finally, we demonstrate computational results obtained with
the proposed residual distribution scheme for several challenging test
problems.
