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Based on the fundamental theory of smoothed-particle hydrodynamics (SPH), a feasible algorithm for fluid–solid coupling on interface is applied to describe the dynamic behavior of fluid and solid by utilizing continuum mechanics governing equations. Numerical simulation is conducted based on the proposed SPH model and the fluid–solid interface coupling algorithm, and good agreement is observed with the experiment results. It is shown in the results that the present SPH model is able to effectively and accurately simulate the free-surface flow of fluid, deformation of the elastic solid and the fluid–solid impacting.

The flow field and the sand flow field constitutive equations are analyzed at first, then the different desert highway numerical models are established by considering the crossroad and by changing the road surface height and air stream flow field, then three kinds of different models with different complex air flow fields are made for simulating the sand ripple formation process by weak coupling of air and sand flow field, and finally the numerical simulations of these models are conducted and the affect process of sand morphology under complex air flow fields are discussed. The results show that under the uniform airflow field, the straight parallel ripple formed and the flared ripple formed in the middle region of the crossroad, and the wavelength of the ripples on the desert highway is bigger than that of the ripples around the road when the road height is higher than that of the sand surface height. Under the nonuniform complex airflow field, the complex curved ripples are formed, and some of the local area, where the whirlwind exits, no ripples are formed.

Wind caused the much sediment fluxes leading to both erosion and deposits in the sandy desertification area, and the much kind of beautiful sandy desert morphologies are formed. This is really crucial to the development of the dynamic behaviour of aeolian transport of sand particles. The sand desert morphologies are representing significant information archives for understanding the desertification problem. Dynamics and numerical modeling provides an essential tool for studying the aeolian transport of sand particle and morphology of sand desert such as ripple and dune. In this study, the mathematical models based on the dynamics are analyzed by considering the several keys as saltation, creep, suspension, avalanche and its threshold condition etc. for sand morphology forming processes. Then due to sand flow field real characteristics, the establishing process of stream flow field are analyzed, and the implication relationships as well as the coupling process between uniform stream flow field and the sand flow field are analyzed. Finally, the sand flow field models is discretized, and different kinds of sandy desert morphology are simulated by considering the sand particle size and mass in fixed, semi-fixed and free sand flow field area.

The sand cover is the main form of sand disaster for the desert highway induced by the wind-blown-sand flow over the highway. As a kind of two-phase flow of air and sand, it is necessary to study the physical principle and the mode of its migration. The Smoothing Particle Hydrodynamic (SPH) method is adopted to simulate the movement of the wind-blown-sand flow. A two dimensional model of the sand cover for desert highway with embankment is built with SPH method. The numerical simulations are carried for different embankment height to investigate the sand cover distribution on the road surface of desert highway. The results show that the migration of sand with wind blow can be well simulated using SPH method and the embankment height is an important factor for controlling sand cover disaster of desert highway.