  In this paper we develop a dual-support smoothed particle hydrodynamics
(DS-SPH) that naturally satisfies the conservation of momentum, angular
momentum and energy when the varying smoothing length is utilized. The DS-SPH
is based on the concept of dual-support, which is introduced to consider the
unbalanced interactions between the particles with different smoothing lengths.
Our DS-SPH formulation can be implemented in traditional SPH with little
changes and improve the computational efficiency. Several numerical examples
are presented to demonstrate the capability of the method.
