# A Consistent Multi-Resolution Smoothed Particle Hydrodynamics Method

## TL;DR

This paper introduces a multi-resolution smoothed particle hydrodynamics (SPH) method for fluid-structure interaction simulations, enabling larger and faster computations by coupling different resolutions without overlap, while maintaining accuracy and stability.

## Contribution

The paper presents a novel multi-resolution SPH approach with direct coupling of subdomains, dynamic particle refinement, and second-order discretization for improved FSI simulation efficiency.

## Key findings

- Method achieves accurate results comparable to single-resolution SPH and finite element solutions.
- Demonstrates improved computational efficiency and larger simulation scales.
- Ensures stability and accuracy through particle regularity and dynamic refinement techniques.

## Abstract

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.