A simple Chimera grid method with an implicit Dirichlet/Neumann coupling scheme for flows with moving boundaries

Abstract

A simple Chimera grid method is developed for complex flows with moving boundaries. Based on the interpolation condition, a coupling strategy is proposed where algebraic equations are reconstructed to couple different domains. With respect to other methods, the coupling of different domains can be accomplished with the employment of any discretization scheme and the iterative process or the iterative solver are avoided. The process of reconstruction is simple to be implemented by the node-by-node replacement, which makes little change on the original code. In addition, the reconstructed system matrix keeps symmetric and positive definite, hence the old solver is appliable. The developed method has a clear physical meaning, namely the transmission condition of Dirichlet/Neumann type. The interpolation condition makes the variable continuous across the interior boundaries, which is the Dirichlet condition, while the Neumann condition is imposed by the reconstruction of the system matrix and the right hand side. For the flows with moving boundaries, this method cannot be applied directly as the interpolation condition varies. The corresponding change on reconstruction of the right hand side is conducted to resolve moving boundaries. Finally, the reliability and the accuracy of the present method are validated by several benchmark problems. The simulation results show that the accuracy of the discretization scheme is not affected by the present coupling strategies.