A stable and conservative coupling of the unsteady compressible navier-stokes equations at interfaces using finite difference and finite volume methods

Peter Eliasson, Jing Gong, Jan Nordström

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Stable and conservative interface boundary conditions are developed for the unsteady compressible Navier-Stokes equations using finite difference and finite volume methods. The finite difference approach is based on summation-by-part operators and can be made higher order accurate with boundary conditions imposed weakly. The finite volume approach is an edge- and dual grid-based approach for unstructured grids, formally second order accurate in space, with weak boundary conditions as well. Stable and conservative weak boundary conditions are derived for interfaces between finite difference methods, for finite volume methods and for the coupling between the two approaches. The three types of interface boundary conditions are demonstrated for two test cases. Firstly, inviscid vortex propagation with a known analytical solution is considered. The results show expected error decays as the grid is refined for various couplings and spatial accuracy of the finite difference scheme. The second test case involves viscous laminar flow over a cylinder with vortex shedding. Calculations with various coupling and spatial accuracies of the finite difference solver show that the couplings work as expected and that the higher order finite difference schemes provide enhanced vortex propagation.

Original languageEnglish
Title of host publicationAIAA Aerospace Sciences Meeting
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624105241
DOIs
Publication statusPublished - 2018
Externally publishedYes
EventAIAA Aerospace Sciences Meeting, 2018 - Kissimmee, United States
Duration: 8 Jan 201812 Jan 2018

Publication series

NameAIAA Aerospace Sciences Meeting, 2018

Conference

ConferenceAIAA Aerospace Sciences Meeting, 2018
Country/TerritoryUnited States
CityKissimmee
Period8/01/1812/01/18

ASJC Scopus subject areas

  • Aerospace Engineering

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