Two dimensional shallow-water flow model with immersed boundary method

This study demonstrates an immersed boundary (IB) method which integrates a depth-averaged two dimensional flow model is proposed to tackle a typical fluid–solid phase problem in fluid dynamics field. The finite-difference scheme with curvilinear coordinate system is employed to discretize the shallow-water flow equations. Lagrangian markers and Eulerian grid are applied to portray the geometric contour of interior boundary and discretize the flow domain, respectively. The Dirac delta function is accordingly conducted to link both Lagrangian and Eulerian coordinate systems. The numerical simulations of single pier are performed and compared to examine the effect of marker’s mesh width, grid size, and the various Dirac delta functions. Experimental data from literatures are compared with numerical results to justify the validity of the proposed IB model. To further demonstrate the model capability, the model is applied to the hypothetical cases of piers in parallel, and compared with theoretical results.

► An immersed boundary method integrates a depth-averaged 2D flow model is proposed.
► The numerical examination of single pier are performed.
► The effects of marker’s mesh width, grid size, Dirac delta functions are examined.
► Experimental data is compared to justify the validity of the proposed model.
► The model is applied to the hypothetical cases and compared with theoretical results.