# Some multilevel decoupled algorithms for a mixed Navier-Stokes/Darcy model

## TL;DR

This paper introduces multilevel decoupled algorithms for a mixed Navier-Stokes/Darcy model, demonstrating their accuracy and efficiency through error analysis and numerical experiments with different discretizations.

## Contribution

It proposes new multilevel decoupled algorithms for the Navier-Stokes/Darcy model, with proven error estimates and validated effectiveness.

## Key findings

- Algorithms achieve accurate approximations as shown by error estimates.
- Numerical experiments confirm the effectiveness of the proposed methods.
- Both first and second order discretizations are successfully implemented.

## Abstract

In this work, several multilevel decoupled algorithms are proposed for a mixed Navier-Stokes/Darcy model. These algorithms are based on either successively or parallelly solving two linear subdomain problems after solving a coupled nonlinear coarse grid problem. Error estimates are given to demonstrate the approximation accuracy of the algorithms. Experiments based on both the first order and the second order discretizations are presented to show the effectiveness of the decoupled algorithms.