On the numerical simulation of non-classical quasi-1D steady nozzle flows: Capturing sonic shocks

Davide Vimercati and Alberto Guardone

Applied Mathematics and Computation, 2018, vol. 319, issue C, 617-632

Abstract: The suitability of Roe-type upwind schemes for the computation of steady quasi-1D flows of non-ideal fluids using explicit integration in the pseudo time is discussed. Based on the particular Roe linearization and entropy fix technique applied, several numerical difficulties can arise in modeling shock waves that are sonic either on the upstream or downstream side of the shock. These so-called sonic shocks typically occur away from stationary points of the cross-sectional area distribution, namely, where the geometrical source term does not vanish. The problem of selecting suitable formulations for the accurate simulation of non-classical quasi-1D steady flows is therefore addressed. Numerical experiments indicate a limited influence of the chosen Roe linearization technique, provided the so-called Property U, allowing the exact representation of steady shocks, is satisfied. Nevertheless, application of standard entropy fixes may either predict an incorrect steady-state transonic expansion neighbouring the sonic shock or even fail to attain a discrete steady state. In the latter case, lack of convergence is due to numerical unbalancing of the flux difference and source term integral over the transonic expansion which occurs in the close proximity of sonic shocks approaching their steady-state position. A simple modification to the synchronous splitting technique of [28] is proposed, which is able to produce the desired steady-state balance and allows substantial improvement in the resolution of sonic shocks.

Keywords: Non-classical gasdynamics; Steady-state flows; Roe scheme; Source terms (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317304940
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:319:y:2018:i:c:p:617-632

DOI: 10.1016/j.amc.2017.07.033

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().