An algorithm for implementing a boundary viscous force with single-layer wall particles based on WCSPH

In numerical simulations of fluid dynamics based on the smoothed particle hydrodynamics (SPH) method, the formula for the viscosity term is always complicated since it is a second order derivative term. In this paper, for Newtonian fluids, a novel formula for the viscous force satisfying the Stokes hypothesis is proposed in the weakly compressible framework. Because of the ease of adopting only a single layer of particles to enforce the boundary condition, the normal flux method is implemented for a solid wall boundary, which should be suitable for complex geometries and thin structures. The normal flux method can mitigate the decrease in numerical accuracy caused by the lack of neighbouring particles at the boundary. Meanwhile, the kernel function at the boundary is modified to satisfy the normalization condition. The accuracy and robustness of the proposed algorithm are verified by a series of cases of numerical fluid simulations, paving the way for SPH simulations coupled with complex thin shell structures for fluid-structure interaction problems.