THE field velocity or grid velocity approach is a method for incorporating unsteady flow conditions via grid movement in computational fluid dynamic simulations. This approach provides a unique methodology for directly calculating aerodynamic responses to step changes in flow conditions. Physically, the grid velocity can be interpreted as the velocity of a grid point in the mesh during the unsteady motion of the boundary surface. For example, the simulation of a step change in angle of attack of an airfoil can be performed by incorporating a step change in vertical grid velocity all over the flow domain. This method effectively decouples the influence of pure angle of attack from that of a pitch rate because the airfoil is not made to pitch, and because the step change is enforced over the entire flow domain uniformly [1]. A similar methodology can be used for simulating responses of an airfoil to step changes in pitch rate and interaction with traveling vertical gusts or convecting vortices [2, 3]. The grid velocity approaches are normally implemented without actually moving the grid. Rather, the time metrics are modified to effectively simulate the motion of the grid. But incorporation of the field velocity approach without actually moving the grid does at times violate the so-called geometric conservation law (especially when there is large variation in the grid velocities between successive grid points). The geometric conservation law (GCL) is used to satisfy the conservative relations of the surfaces and volumes of the control cells in moving meshes. Primarily, the GCL states that the volumetric increment of a moving cell must be equal to the sum of the changes along the surfaces that enclose the volume. Thomas and Lombard [4] were the first to recognize the necessity of satisfying the geometric conservation laws simultaneously with other physical conservations when solving moving mesh problems. They proposed a differential form of the GCL which needs to be solved along with the conservative variables. More modern approaches [5–7] efficiently compute the space and time metrics in a manner that implicitly guarantees the satisfaction of the GCL. One of the highly unsteady flow problems of practical interest is computing the flow field around a helicopter rotor blade undergoing aeroelastic deformations. The unsteadiness in flow field is primarily caused by the periodic blade motions and the wake induced inflow. Resorting to a global multiblock, overset mesh type approach (which models all the rotor blades) limits the practicality of such a calculation because of high computational overheads. Also one needs to carefully tune the grid spacings to preserve the trailed vortices. The use of a local single block approach (which models a single rotor blade) requires the inclusion of the influences of a trailed vortex wake, whose geometry is computed from using an external calculation (usually a Lagrangian vortex lattice approach [8]). The field velocity approach may be used for wake inclusion in such cases. In this approach, there is a dynamic real movement of the mesh because of the aeroelastic blade deformations and an apparent movement of the mesh because of the use of the field velocity approach [9]. This poses a unique challenge for preserving the GCL. The computation of space and time metrics should be performed consistently to maintain conservation and hence preserve accuracy. The objectives of this research effort are threefold. The first objective is to demonstrate the capabilities of the grid velocity approach for the simulation of unsteady flow environments. The second objective is to develop methodologies for computing 4th order accurate space metrics and …