# Strongly coupled simulation of incompressible fluid and rigid bodies with velocity-based constraints using particle method

## TL;DR

This paper introduces a particle-based, velocity-formulated method for strongly coupling incompressible fluid and rigid bodies, ensuring compatibility of constraints and enabling complex simulations.

## Contribution

It presents a novel velocity-based formulation and a unified approach to simulate incompressible fluids and rigid bodies with strong coupling using particle methods.

## Key findings

- Successfully simulates dam-break and hydrostatic pressure scenarios.
- Demonstrates stable interaction between fluid and rigid bodies.
- Validates the method with complex scene simulations.

## Abstract

This paper presents a novel particle method to compute strongly coupled incompressible fluid and rigid bodies. The method adopts a velocity-based formulation and utilizes the linear complementarity problem for the incompressibility constraint. Since all the constraints for incompressibility, inter-rigid-body contacts, and interaction between incompressible fluid and rigid bodies are mathematically compatible, strongly coupled simulation is achieved using the method, where the shapes of the rigid bodies are represented by particles as well. The abstract concept of velocity-based constraints is presented, which generalizes the formulations of the incompressibility constraint and inter-rigid-body contacts and provides a generic way to achieve strongly coupled simulation. Several numerical examples are presented to verify the method, which includes rigid-body computation, hydrostatic pressure, dam-break computation, and circular parch computation for incompressible fluid, buoyancy and seesaw computation for interaction of incompressible fluid and rigid bodies, and complex-scene computation for overall behavior and stability.