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

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摘要

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.

论文关键词:Non-classical gasdynamics,Steady-state flows,Roe scheme,Source terms

论文评审过程:Received 29 September 2016, Revised 14 March 2017, Accepted 10 July 2017, Available online 3 August 2017, Version of Record 31 October 2017.

论文官网地址:https://doi.org/10.1016/j.amc.2017.07.033