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 two numerical experiments outlined in the manuscript titled "On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow". The incompressible Navier-Stokes equations addressed in this manuscript 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 manuscript. 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 two experiments detailed in the manuscript showcase how the convergence of various implicit Runge-Kutta (IRK) methods, applied to solve the system, is influenced by different implementation schemes.

Steps to reproduce

Please find the README.html in the respository for reproduction steps.

Institutions

• University of Notre Dame
• Nanjing Tech University

Categories

Licence