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Numerical Methods for Inviscid Flow Equations
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
Shock-capturing schemes are the most widely used techniques for computing inviscid flows with shocks. In this approach, the Euler equations are cast in conservation-law form, and any shock waves or other discontinuities are computed as part of the solution. The shock waves predicted by these methods are usually smeared over several mesh intervals, but the simplicity of the approach may outweigh the slight compromise in results compared to the more elaborate shock-fitting schemes. Classical shock-capturing methods have the disadvantage that very strong shocks will cause the methods to fail. This failure is usually evidenced by oscillations. Computations in hypersonic flow with very strong shocks typically lead to the appearance of negative pressures and subsequent divergence of the solution during the time-dependent computation process. In addition to this problem, higher-order schemes tend to produce oscillations in the solution. However, these methods are useful and will be modified in later sections to avoid these difficulties. The alternative approach is to fit each shock wave as a discontinuity and solve for the discontinuity as part of the solution. This shock-fitting approach is very elegant and produces shocks that are truly discontinuous. Unfortunately, the procedure for general shock fitting in three dimensions with multiple shocks is extremely complex, and as a result, the use of shock fitting is usually limited to fitting shocks at boundaries.
The elusive topic of rainfall-induced surge waves in rivers: lessons from canyon accidents
Published in International Journal of River Basin Management, 2022
The numerical integration here performed is particularly meaningful for the present purposes because: it is characterized by relevant numerical diffusion effects, that would tend to counteract the steepening tendency and the development of the shock;the shock-capturing methods can simulate steep front waves and shocks without introducing further conditions or procedures. Previous calculations related to hydrograph steepening (Collischonn et al., 2017; Ponce & Windingland, 1985) are not based on shock-capturing methods, that have rather been used for simulating surge wave propagation in sewers (e.g. Lautenbach et al., 2008);the complete form of the unsteady flow equations here adopted ensure that the effects of approximations (including kinematic hypothesis) are ruled out.
Dynamic mode decomposition of supersonic turbulent pipe flow with and without shock train
Published in Journal of Turbulence, 2020
G. Srinivasan, Susila Mahapatra, Kalyan P. Sinhamahapatra, Somnath Ghosh
However, there are very few LES studies of shock–turbulence interaction in internal flows. Koo and Raman [14] studied shock–turbulence interaction in a supersonic inlet isolator using LES. Different shock capturing methods like hyperviscosity approach and weighted essentially non-oscillatory (WENO) schemes were used and compared. LES of shock train in a constant area supersonic isolator with rectangular cross-section has been performed by Morgan and Lele [15] and the results were compared qualitatively with experiments carried out at a higher Reynolds number. Using the ALDM approach, Quaatz et al. [16] studied shock train in a Laval nozzle with rectangular cross-section. Mahapatra et al. [17] studied shock train phenomena in supersonic pipe and divergent–convergent diffuser flows with isothermal walls by means of LES. The shock train showed low-frequency oscillations which was demonstrated and quantified in the study by means of pressure traces and power-spectral density.
On the Origins of Lagrangian Hydrodynamic Methods
Published in Nuclear Technology, 2021
Nathaniel R. Morgan, Billy J. Archer
An interesting historical point is at the end of Peierls’ March 28, 1944 letter to von Neumann, he suggested that an artificial viscosity could be used to slightly smear the shock discontinuity, making it numerically tractable.25 Richtmyer implemented this idea in 1948 (Refs. 27 and 44). He and von Neumann made this the standard method for handling shocks in Lagrangian hydrodynamic codes with their 1950 journal paper.24 This is known as a smeared shock method or shock-capturing method. The use of artificial viscosity allowed the intrinsic treatment of strong shocks without undue smearing of the weak shocks. The details on Richtmyer’s scheme will now be discussed.