Replication code and data: On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow

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.

本仓库包含复现论文中所述三项数值实验所需的代码与数据集。论文题为《含非定常入流的不可压缩纳维-斯托克斯（Navier-Stokes）方程的隐式龙格-库塔方法收敛性研究》，作者为Y. Cai、J. Wan与A. Kareem，发表于《计算物理期刊》（Journal of Computational Physics），DOI链接：https://doi.org/10.1016/j.jcp.2024.113627。本文所研究的不可压缩纳维-斯托克斯方程，属于通过有限体积法或有限差分法进行空间离散后得到的半离散纳维-斯托克斯系统。本文针对该系统的时间求解提出了一种隐式龙格-库塔（implicit Runge-Kutta）格式，该格式不仅缓解了各类隐式龙格-库塔方法常面临的阶数缩减问题，同时即便针对非刚性精度格式，也能严格满足无散约束条件。本文详述的三项实验展示了应用于该系统求解的各类隐式龙格-库塔（IRK）方法的收敛性如何受不同实现方案的影响。