  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,
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. We also demonstrate the accuracy of the proposed
scheme by using it to solve the flow past a circular cylinder. 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.
