التفاصيل البيبلوغرافية
| العنوان: |
Hydrodynamics of a discrete conservation law. |
| المؤلفون: |
Sprenger, Patrick1 (AUTHOR) sprenger@ucmerced.edu, Chong, Christopher2 (AUTHOR), Okyere, Emmanuel2 (AUTHOR), Herrmann, Michael3 (AUTHOR), Kevrekidis, P. G.4 (AUTHOR), Hoefer, Mark A.5 (AUTHOR) |
| المصدر: |
Studies in Applied Mathematics. Nov2024, Vol. 153 Issue 4, p1-48. 48p. |
| مصطلحات موضوعية: |
MODULATION theory, RIEMANN-Hilbert problems, SHOCK waves, CONSERVATION laws (Physics), HYDRODYNAMICS |
| مستخلص: |
The Riemann problem for the discrete conservation law 2u̇n+un+12−un−12=0$2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi‐continuum approximation, and numerical simulations. A surprisingly elaborate set of solutions to this simple discrete regularization of the inviscid Burgers' equation is obtained. In addition to discrete analogs of well‐known dispersive hydrodynamic solutions—rarefaction waves (RWs) and dispersive shock waves (DSWs)—additional unsteady solution families and finite‐time blowup are observed. Two solution types exhibit no known conservative continuum correlates: (i) a counterpropagating DSW and RW solution separated by a symmetric, stationary shock and (ii) an unsteady shock emitting two counterpropagating periodic wavetrains with the same frequency connected to a partial DSW or an RW. Another class of solutions called traveling DSWs, (iii), consists of a partial DSW connected to a traveling wave comprised of a periodic wavetrain with a rapid transition to a constant. Portions of solutions (ii) and (iii) are interpreted as shock solutions of the Whitham modulation equations. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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