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

Published: 26 February 2024| Version 1 | DOI: 10.17632/vnfkpcczpb.1
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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.

Files

Steps to reproduce

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

Institutions

University of Notre Dame, Nanjing Tech University

Categories

Computational Fluid Dynamics

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