Extension of local domain-free discretization method to simulate 3D flows with complex moving boundaries

This paper is the first endeavor to present the local domain-free discretization (DFD) method for the solution of the three-dimensional Navier–Stokes equations. The computational domain may contain complex moving boundaries. The strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. The functional values at the exterior dependent points are evaluated by the approximate form of solution near the boundary. Compared to the previous work, the tedious task of constructing new interpolation tetrahedrons is eliminated, and this reduces the complexity of DFD implementation. An efficient algorithm for classifying mesh points is also presented. Simulation of flow around a stationary sphere is used to validate the numerical method, and three distinct flow regimes have been obtained with varied Reynolds numbers of up to 300. The ability of the method for flows with complex moving boundary is demonstrated by simulating flows over an undulating fish-like body. The results of force coefficient, structure of wake patterns and propulsive efficiency at critical Strouhal number have been presented. All predictions show a good agreement with the reference data.

► The local DFD method is extended to solve 3D N–S equations with moving boundaries.
► Compared to the previous work, the complexity of DFD implementation is reduced.
► An efficient algorithm for classifying mesh points is presented.
► The ability of DFD is demonstrated by simulating flows over an undulating fish.