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。相关论文中文译题为《带非定常入射流的不可压缩Navier-Stokes方程的隐式龙格-库塔方法收敛性》，英文原题为"On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow"，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Navier-Stokes方程对应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Navier-Stokes系统。该论文针对该系统的时域求解提出了一种隐式龙格-库塔格式，所提格式不仅缓解了各类隐式龙格-库塔方法常遭遇的阶数缩减问题，即便对于非刚性精确格式，也能严格满足无散约束条件。论文中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。