This paper presents a computational scheme solely based on the Rankine-Hugoniot shock relations to describe the propagation of strongly-nonlinear waves in fluids, the amplitude of which is so great that second-order approximations such as the weak shock theory and the Burgers equation do not apply. The Rankine-Hugoniot relations are three algebraic equations connecting the flow variables (pressure, density, particle velocity, and energy) across a shock. What is not well known is that the Rankine-Hugoniot relations can be used to compute the nonlinear evolution of the continuous segment of a wave, if the continuous segment can be approximated by a succession of infinitesimal compression shocks [Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002), pp. 85-86]. We further extend this idea to the other continuous segment that can be discretized into a series of infinitesimal rarefaction shocks. The discretization of a waveform and the subsequent application of the Rankine-Hugoniot relations lead to a Riemann problem that conveniently treats continuous segments and real shocks in the same manner. Our computational scheme distinguishes itself from the conventional Riemann problem in that shocks are treated as particles, which facilitates an enormous saving in computation time. The scheme is verified against the 1-D Riemann solver for the case of strong blast waves.
|Title of host publication||Recent Developments in Nonlinear Acoustics|
|Subtitle of host publication||20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum|
|Editors||Victor W. Sparrow, Didier Dragna, Philippe Blanc-Benon|
|Publisher||American Institute of Physics Inc.|
|Publication status||Published - 2015 Oct 28|
|Event||20th International Symposium on Nonlinear Acoustics, ISNA 2015, including the 2nd International Sonic Boom Forum, ISBF 2015 - Ecully, Lyon, France|
Duration: 2015 Jun 29 → 2015 Jul 3
|Name||AIP Conference Proceedings|
|Other||20th International Symposium on Nonlinear Acoustics, ISNA 2015, including the 2nd International Sonic Boom Forum, ISBF 2015|
|Period||15/6/29 → 15/7/3|
Bibliographical notePublisher Copyright:
© 2015 AIP Publishing LLC.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)