  In Lagrangian meshfree methods, the underlying spatial discretization,
referred to as a point cloud or a particle cloud, moves with the flow velocity.
In this paper, we consider different numerical methods of performing this
movement of points or particles. The movement is most commonly done by a first
order method, which assumes the velocity to be constant within a time step. We
show that this method is very inaccurate and that it introduces volume and mass
conservation errors. We further propose new methods for the same which
prescribe an additional ODE system that describes the characteristic velocity.
Movement is then performed along this characteristic velocity. The first new
way of moving points is an extension of mesh-based streamline tracing ideas to
meshfree methods. In the second way, the movement is done based on the
difference in approximated streamlines between two time levels, which
approximates the pathlines in unsteady flow. Numerical comparisons show these
method to be vastly superior to the conventionally used first order method.
