Hydrodynamic impact of free-surface viscoelastic flows on mildly inclined planes: A 3D multiphase DNS study

Free-surface viscoelastic flow past obstacles is investigated through three-dimensional direct numerical simulations (DNS) of the full Navier–Stokes equations. In contrast to previous studies, the present work explicitly incorporates the effect of surface waves, which had been previously neglected, and systematically examines their influence on the flow structures and hydrodynamic impact forces. The numerical methodology is validated through comparison with analytical solutions for unidirectional flow as well as with an independent solver for multiphase viscoelastic fluids employing different numerical formulations. Numerical accuracy and convergence are further confirmed through a mesh refinement study. The results show that the flow pattern around the obstacle undergoes a transition from a smooth standing wave to a bow shock wave as the Froude number increases. For a fixed Froude number, the drag coefficient increases with the Weissenberg number, indicating a pronounced viscoelastic drag enhancement. However, this enhancement diminishes as the Froude number increases. At sufficiently large Weissenberg numbers, the drag coefficient approaches an asymptotic value that depends primarily on the Froude number and obstacle shape. Four obstacle geometries are examined: circular prism, square prism, triangular prism, and elliptical prism. Under identical inflow conditions, the square prism produces the largest drag coefficient and run-up height, whereas the triangular prism results in the smallest drag coefficient and run-up height.