Replication code and data: On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow
Description
This repository contains the code and data necessary for replicating three numerical experiments outlined in the paper: "On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow", Y. Cai, J. Wan and A. Kareem, Journal of Computational Physics, https://doi.org/10.1016/j.jcp.2024.113627. The incompressible Navier-Stokes equations addressed in this paper pertain to the semi-discrete Navier-Stokes system, resulting from either finite volume or finite difference spatial discretization. An implicit Runge-Kutta scheme for the temporal solution of this system is proposed in the paper. The proposed scheme not only alleviates the order reduction encountered by various implicit Runge-Kutta methods, but also ensures the exact enforcement of the divergence-free constraint, even for non-stiffly accurate methods. The three experiments detailed in the paper showcase how the convergence of various implicit Runge-Kutta (IRK) methods, applied to solve the system, is influenced by different implementation schemes.
Files
Steps to reproduce
Please find the README.html in the respository for reproduction steps.
Institutions
- University of Notre Dame
- Nanjing Tech University