How to train your solver: Verification of boundary conditions for smoothed particle hydrodynamics

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 as well as inlet and outlet boundary conditions. However, error estimation and the formal rates of convergence for these methods have not been carefully discussed or examined. In this paper, we use the method of manufactured solutions to verify the convergence properties of a variety of commonly employed 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.

Automated summary

In this paper, the convergence properties of commonly used solid, inlet, and outlet boundary implementations are verified using the method of manufactured solutions. A convergent WCSPH scheme along with suitable methods for implementing the boundary conditions are proposed based on the convergence offered by these methods. The accuracy of the proposed scheme is demonstrated by solving the flow past a circular cylinder, paving the way for the accurate and efficient simulation of fluid flows using the SPH method.