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Conservation Laws and a Compact Quasi-Gasdynamic System

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Abstract

Based on the application of conservation laws, a compact quasi-gasdynamic system, which was previously obtained using a kinetic model, is derived. The possibility of using algorithms previously used to solve the Navier–Stokes equations to solve this system is discussed.

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Notes

  1. Here, for simplicity, we assume that the field of external forces affectin the change \(\bar {\xi }\) is absent.

  2. The choice \(\tau \) as the minimum scale \(~\Delta t~\) is not accidental, since the establishment of gas-dynamic parameters occurs in a time period that is not smaller than the characteristic time between molecular collisions \(\tau \).

  3. The advantages of condition (37) over the stability condition for explicit schemes for parabolic equations \((\Delta t \lesssim {{h}^{2}})\) are especially evident with detailed spatial approximations (small h), which are implemented on high-performance computing systems.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    B. N. Chetverushkin, A. E. Luzkiy & V. P. Osipov

  2. Plekhanov Russian University of Economics, 115093, Moscow, Russia

    V. P. Osipov

Authors
  1. B. N. Chetverushkin
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  2. A. E. Luzkiy
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  3. V. P. Osipov
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Correspondence to B. N. Chetverushkin, A. E. Luzkiy or V. P. Osipov.

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Chetverushkin, B.N., Luzkiy, A.E. & Osipov, V.P. Conservation Laws and a Compact Quasi-Gasdynamic System. Math Models Comput Simul 12, 546–552 (2020). https://doi.org/10.1134/S2070048220040055

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  • DOI: https://doi.org/10.1134/S2070048220040055

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