Modelling, asymptotic analysis and simulation of the gas dynamics in a chimney. (English) Zbl 1274.35282
Summary: This paper presents a one dimensional model for the gas dynamics in a chimney. This is a prototype example of a small Mach number flow with strong heat sources. Due to the small Mach number of the gas flow an asymptotic model is derived from a fully compressible model, which then is compared to the original model and to the often used Boussinesq approximation. The Boussinesq approximation is shown to be inappropriate for this application, whereas the small Mach number asymptotic model we propose is shown to be a very good approximation. In particular it allows very fast numerical simulations. Finally, all this is underlined by numerical simulations where we validate the various models.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
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