Abstract: When a lander gradually approaches a dusty lunar surface, the plume from the descent engine impinges on the ground and entrains loose regolith into a high velocity spray.  These dust sprays can be problematic for the approaching spacecraft as well as for pre-existing structures on the moon.  The modeling of such flows encompasses a variety of complex phenomena such as highly compressible viscous flow, transition from continuum to free molecular flow, soil erosion, and fully coupled gas-dust motions.  In the present work, the Navier-Stokes solver DPLR is used in the near-field where continuum assumptions are valid but kinetic solvers are prohibitively expensive.  The continuum solution is then coupled to a direct simulation Monte Carlo solver that simulates the flow as it becomes rarefied and continuum assumptions break down.  Fully coupled dust scouring and transport models have been developed.  The dust sprays are characterized for different hovering altitudes and levels of thrust.  The simulation results qualitatively agree with Apollo observations for particle speeds and dust sheet inclination angles.  The sensitivity to model parameters is studied and the dust motion is found to be especially sensitive to the assumed inelasticity of grain-grain collisions.  High velocity dust sprays may be unavoidable and mitigation techniques are necessary to protect pre-existing hardware or residents.  One mitigation technique is to use a lunar fence or berm to deflect the dust around sensitive structures.  The interactions between the dust spray with such a fence are analyzed for different fence heights, placements, angles, and restitution coefficients.  Future landers may use multi-engine configurations that result in 3-dimensional flow structures.  A four engine lander has been simulated and the plume-plume and plume-surface interactions create focused jets of dust.  This engine configuration has been simulated for several hovering altitudes and changes to the dust sprays are discussed.