We seek to accelerate and increase the size of simulations for fluid-structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way fluid-solid coupling.To this end, we propose a multi-resolution smoothed particle hydrodynamics (SPH) approach in which subdomains of different resolutions are directly coupled without any overlap region. The second-order consistent discretization of spatial differential operators is employed to ensure the accuracy of the proposed method. As SPH particles advect with the flow, a dynamic SPH particle refinement/coarsening is employed via splitting/merging to maintain a predefined multi-resolution configuration. Particle regularity is enforced via a particle-shifting technique to ensure accuracy and stability of the Lagrangian particle-based method embraced. The convergence, accuracy, and efficiency attributes of the new method are assessed by simulating four different flows. In this process, the numerical results are compared to the analytical, finite element, and consistent SPH single-resolution solutions. We anticipate that the proposed multi-resolution method will enlarge the class of SPH-tractable FSI applications.volume methods for FSI. The expectation is that APR will maintain the accuracy of the SPH solution while improving efficiency and increasing the size of the problem solved.In this context, several multi-resolution SPH methods have been proposed, e.g., [19,20,21,22,23,24,25]. In these efforts, SPH particles were distributed according to a pre-defined multi-resolution configuration. What set these approaches apart was the coupling between regions of different resolutions and thereby the accuracy and continuity of the numerical solution at and near the interface. In [26], the same large smoothing length was used for both the low-and high-resolution regions. This enhanced the accuracy attribute of the solution in some degree but led to a large number of neighbors for the particles in the high-resolution region. Thus, performance was hurt, which defeated APR's purpose. In [23,27,24], each region had its own smoothing length, which reduced the computational cost substantially. However, using an inconsistent SPH discretization, the numerical solution near the interface lacked accuracy, an artifact that became worse as the ratio of the two resolutions increased. This point will be demonstrated in §3.1. To tackle this issue, an approach promoting different-resolution subdomains connected via an overlap region was described in [25]. Therein, the overlap region was employed to exchange state information and fluxes. At each time step, the solutions in the two subdomains were brought in sync via the overlap region by an iterative process. The authors investigated the sensitivity of numerical accuracy with respect to the thickness of the overlap region; a minimum thickness of the overlap region was determined numerically. On the upside, the approach can employ a different time step fo...
