A Consistent Multi-Resolution Smoothed Particle Hydrodynamics Method

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.Comment: 27 pages, 34 figure

A Consistent Spatially Adaptive Smoothed Particle Hydrodynamics Method for Fluid-Structure Interactions

A new consistent, spatially adaptive, smoothed particle hydrodynamics (SPH) method for Fluid-Structure Interactions (FSI) is presented. The method combines several attributes that have not been simultaneously satisfied by other SPH methods. Specifically, it is second-order convergent; it allows for resolutions spatially adapted with moving (translating and rotating) boundaries of arbitrary geometries; and, it accelerates the FSI solution as the adaptive approach leads to fewer degrees of freedom without sacrificing accuracy. The key ingredients in the method are a consistent discretization of differential operators, a \textit{posteriori} error estimator/distance-based criterion of adaptivity, and a particle-shifting technique. The method is applied in simulating six different flows or FSI problems. The new method's convergence, accuracy, and efficiency attributes are assessed by comparing the results it produces with analytical, finite element, and consistent SPH uniform high-resolution solutions as well as experimental data.Comment: 27 pages, 17figure

A Stable SPH Discretization of the Elliptic Operator with Heterogeneous Coefficients

Smoothed particle hydrodynamics (SPH) has been extensively used to model high and low Reynolds number flows, free surface flows and collapse of dams, study pore-scale flow and dispersion, elasticity, and thermal problems. In different applications, it is required to have a stable and accurate discretization of the elliptic operator with homogeneous and heterogeneous coefficients. In this paper, the stability and approximation analysis of different SPH discretization schemes (traditional and new) of the diagonal elliptic operator for homogeneous and heterogeneous media are presented. The optimum and new discretization scheme is also proposed. This scheme enhances the Laplace approximation (Brookshaw's scheme (1985) and Schwaiger's scheme (2008)) used in the SPH community for thermal, viscous, and pressure projection problems with an isotropic elliptic operator. The numerical results are illustrated by numerical examples, where the comparison between different versions of the meshless discretization methods are presented

A spatially adaptive high-order meshless method for fluid-structure interactions

We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS) discretization used in this work has been previously demonstrated to provide high-order compatible discretization of the Stokes and Darcy problems, offering a high-fidelity simulation tool for problems with moving boundaries. The meshless nature of the discretization is particularly attractive for adaptive h-refinement, especially when resolving the near-field aspects of variables and point singularities governing lubrication effects in fluid-structure interactions. We demonstrate that the resulting spatially adaptive GMLS method is able to achieve optimal convergence in the presence of singularities for both the div-grad and Stokes problems. Further, we present a series of simulations for flows of colloid suspensions, in which the refinement strategy efficiently achieved highly accurate solutions, particularly for colloids with complex geometries.Comment: 21 pages, 20 figure