scholarly journals Simulation of multiple shock-shock interference using implicit anti-diffusive WENO schemes

2009 ◽  
pp. n/a-n/a
Author(s):  
Tsang-Jen Hsieh ◽  
Ching-Hua Wang ◽  
Jaw-Yen Yang
Keyword(s):  
Weno Schemes ◽  
Multiple Shock ◽  
Shock Interference

Multiple shock-shock interference on a cylindrical leading edge

AIAA Journal ◽  
1992 ◽  
Vol 30 (8) ◽  
pp. 2073-2079 ◽  
Author(s):  
Allan R. Wieting
Keyword(s):  
Leading Edge ◽  
Multiple Shock ◽  
Shock Interference

Simulation of multiple shock-shock interference patterns on a cylindrical leading edge

AIAA Journal ◽  
1996 ◽  
Vol 34 (4) ◽  
pp. 764-771 ◽  
Author(s):  
Kwen Hsu ◽  
Ijaz H. Parpia
Keyword(s):  
Leading Edge ◽  
Multiple Shock ◽  
Shock Interference

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Acta Numerica ◽  
2020 ◽  
Vol 29 ◽  
pp. 701-762
Author(s):  
Chi-Wang Shu
Keyword(s):  
Main Idea ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Approximation Procedure ◽  
Discontinuous Solutions ◽  
Weno Schemes ◽  
Convection Diffusion ◽  
Different Types ◽  
Basic Ideas ◽  
Weighted Eno

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

Dynamical behavior of the Richtmyer–Meshkov instability-induced turbulent mixing under multiple shock interactions

2017 ◽  
Vol 95 (8) ◽  
pp. 671-681 ◽  
Author(s):  
Tao Wang ◽  
Gang Tao ◽  
Jingsong Bai ◽  
Ping Li ◽  
Bing Wang ◽  
...  
Keyword(s):  
Turbulent Mixing ◽  
Compression Wave ◽  
Dynamical Behavior ◽  
Characteristic Scale ◽  
Mixing Zone ◽  
Shock Interactions ◽  
Scale Parameters ◽  
Eddy Simulation ◽  
Negative Exponential ◽  
Multiple Shock

The dynamical behavior of Richtmyer–Meshkov instability-induced turbulent mixing under multiple shock interactions is investigated by large-eddy simulation. After the initial shockwave–interface interaction, the transmitted wave reverberates between the accelerated interface and the end-wall of the shock tube to form a process of multiple shock interactions. The turbulent mixing zone grows in a different manner under each of the impingements. After the initial shock, it grows as a power law of time. After the reshock and the impingement of the reflected rarefaction wave, it grows with time as a different negative exponential law. When the impingement of the reflected compression wave completes, it grows approximately in a linear fashion. The statistical quantities in the turbulent mixing zone evolve with time in a similar way under multiple impingements, and after the impingement of the reflected compression wave, they all decay asymptotically. Therefore, the turbulent mixing zone behaves in a statistically self-similar pattern. Even though the impingements of different waves result in different abrupt changes of the characteristic scale parameters of mixing turbulence, as a whole, the characteristic scales present a feature of growth, and the characteristic-scale Reynolds numbers present a feature of decay. The mixing flow is continuously anisotropic, yet the anisotropy weakens gradually. Therefore the development of turbulent mixing presents a trend of isotropy.

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