In this research work, a constitutive mathematical review has been carried out to study the application of smoothed-particle hydrodynamics (SPH) in the modeling of geophysical flows like landslide, debris flows and stability failure problems across the world with particular focus on the landslide-associated geohazards happening in the southern region of Luxembourg. A particular interest is drawn to this region due to the research position taken by Stefan Van Baars suggesting the sufficiency of using friction angle of the geophysical flow-prone southern region to model landslide problems. This position invariably suggests that to model geophysical flows in any other region faced with this problem, friction angle data should have been enough. Meanwhile the present study has presented that climate factors and soil behavior variables beyond friction angle are required to solve geophysical flow problems and proposed the mathematical SPH technique as being the most efficient method to model geophysical flow problems due to its versatility and flexibility. Also, the (SPH) method can be used to simulate slope movements with large deformation and requires comprehensive profiling of the environmental and field data of the studied region. Generally, the present research has shown from previous efforts made to solve geophysical flow problems by using SPH, that groundwater flow, pore pressure changes and precipitation-induced infiltration are major factors causing these geohazards if unchecked.