# An immersed method based on cut-cells for the simulation of 2D incompressible fluid flows past solid structures

## TL;DR

This paper introduces a cut-cell method for simulating 2D incompressible flows around solid obstacles, combining finite volume discretization with a MAC scheme on Cartesian grids, demonstrating efficiency at various Reynolds numbers.

## Contribution

The paper presents a novel immersed boundary method using cut-cells and MAC scheme for efficient 2D incompressible flow simulation around static and moving obstacles.

## Key findings

- Effective simulation of flow around a circular cylinder at Re=1000 and 3000.
- Successful application to flow around a moving rigid body at Re=800.
- Validation of the method's efficiency and accuracy through numerical results.

## Abstract

We present a cut-cell method for the simulation of 2D incompressible flows past obstacles. It consists in using the MAC scheme on cartesian grids and imposing Dirchlet boundary conditions for the velocity field on the boundary of solid structures following the Shortley-Weller formulation. In order to ensure local conservation properties, viscous and convecting terms are discretized in a finite volume way. The scheme is second order implicit in time for the linear part, the linear systems are solved by the use of the capacitance matrix method for non-moving obstacles. Numerical results of flows around an impulsively started circular cylinder are presented which confirm the efficiency of the method, for Reynolds numbers 1000 and 3000. An example of flows around a moving rigid body at Reynolds number 800 is also shown, a solver using the PETSc-Library has been prefered in this context to solve the linear systems.