Identifying second order accurate boundary conditions for WCSPH

The weakly compressible smoothed particle hydrodynamics (WCSPH) method has been employed to simulate various physical phenomena involving fluids and solids. Various methods have been proposed to implement the solid wall, and inlet/outlet and other boundary conditions. However, error estimation and the formal rates of convergence for these methods have not been discussed or examined carefully. In this paper, we use the method of manufactured solution (MMS) to verify the convergence properties of a variety of commonly employed of various solid, inlet, and outlet boundary implementations. In order to perform this study, we propose various manufactured solutions for different domains. On the basis of the convergence offered by these methods, we systematically propose a convergent WCSPH scheme along with suitable methods for implementing the boundary conditions. Along with other recent developments in the use of adaptive resolution, this paves the way for accurate and efficient simulation of incompressible or weakly-compressible fluid flows using the SPH method.