Analytical solution of double-Mach reflection

AIAA Journal ◽  
1980 ◽  
Vol 18 (9) ◽  
pp. 1036-1043 ◽  
Author(s):  
G. Ben-Dor
Keyword(s):  
Analytical Solution ◽  
Mach Reflection ◽  
Double Mach Reflection

scholarly journals On Alternative Setups of the Double Mach Reflection Problem

2018 ◽  
Vol 78 (2) ◽  
pp. 1291-1303 ◽  
Author(s):  
U. S. Vevek ◽  
B. Zang ◽  
T. H. New
Keyword(s):  
Mach Reflection ◽  
Double Mach Reflection

scholarly journals Comparison of a modified large-particle method with some high resolution schemes. Two-Dimensional test problems

2019 ◽  
pp. 337-345
Author(s):  
Д.В. Садин ◽  
Б.В. Беляев ◽  
В.А. Давидчук
Keyword(s):  
High Resolution ◽  
Mach Reflection ◽  
Particle Method ◽  
Test Problems ◽  
Nonlinear Correction ◽  
Smooth Solutions ◽  
High Resolution Schemes ◽  
Double Mach Reflection ◽  
Computational Properties ◽  
Second Order Of Approximation

Исследуются вычислительные свойства предложенной ранее новой модификации метода крупных частиц на основе нелинейной коррекции искусственной вязкости на первом (эйлеровом) этапе и гибридизации потоков на втором (лагранжевом и заключительном) этапе, дополненной двухшаговым алгоритмом РунгеКутты по времени. Метод обладает вторым порядком аппроксимации по пространству и времени на гладких решениях. На примере тестовых задач сверхзвукового потока газа в канале со ступенькой и двойного маховского отражения подтверждена работоспособность и вычислительная эффективность метода в сравнении с современными схемами высокой разрешающей способности. A number of computational properties of the previously proposed new modification of a largeparticle method are studied on the basis of a nonlinear correction of artificial viscosity at the first (Eulerian) stage and a hybridization of fluxes at the second (Lagrangian and final) stage supplemented by a twostep RungeKutta algorithm in time. The method has a second order of approximation in space and time on smooth solutions. The computational efficiency of the method is shown compared to several modern high resolution schemes using the forward facing step problem and the double Mach reflection problem.

Piecewise Polynomial Mapping Method and Corresponding WENO Scheme with Improved Resolution

2015 ◽  
Vol 18 (5) ◽  
pp. 1417-1444 ◽  
Author(s):  
Qin Li ◽  
Pengxin Liu ◽  
Hanxin Zhang
Keyword(s):  
Riemann Problem ◽  
Mach Reflection ◽  
Mapping Function ◽  
Mapping Method ◽  
Weno Scheme ◽  
Polynomial Mapping ◽  
Piecewise Polynomial ◽  
Piecewise Polynomial Function ◽  
Double Mach Reflection ◽  
Fifth Order

AbstractAbstract. The method of mapping function was first proposed by Henrick et al. [J. Comput. Phys. 207:542-547 (2005)] to adjust nonlinear weights in [0,1] for the fifth order WENO scheme, and through which the requirement of convergence order is satisfied and the performance of the scheme is improved. Different from Henrick’s method, a concept of piecewise polynomial function is proposed in this study and corresponding WENO schemes are obtained. The advantage of the new method is that the function can have a gentle profile at the location of the linear weight (or the mapped nonlinear weight can be close to its linear counterpart), and therefore is favorable for the resolution enhancement. Besides, the function also has the flexibility of quick convergence to identity mapping near two endpoints of [0,1], which is favorable for improved numerical stability. The fourth-, fifth- and sixth-order polynomial functions are constructed correspondingly with different emphasis on aforementioned flatness and convergence. Among them, the fifth-order version has the flattest profile. To check the performance of the methods, the 1-D Shu-Osher problem, the 2-D Riemann problem and the double Mach reflection are tested with the comparison of WENO-M, WENO-Z and WENO-NS. The proposed new methods show the best resolution for describing shear-layer instability of the Riemann problem, and they also indicate high resolution in computations of double Mach reflection, where only these proposed schemes successfully resolved the vortex-pairing phenomenon. Other investigations have shown that the single polynomial mapping function has no advantage over the proposed piecewise one, and it is of no evident benefit to use the proposed method for the symmetric fifth-order WENO. Overall, the fifth-order piecewise polynomial and corresponding WENO scheme are suggested for resolution improvement.

Transverse waves in numerical simulations of cellular detonations

2001 ◽  
Vol 447 ◽  
pp. 31-51 ◽  
Author(s):  
GARY J. SHARPE
Keyword(s):  
Numerical Simulations ◽  
Triple Point ◽  
Mach Reflection ◽  
Physical Structure ◽  
Structure Evolution ◽  
Transverse Waves ◽  
Strong Transverse ◽  
Cellular Detonations ◽  
Double Mach Reflection ◽  
Steady Detonation

In this paper the structure of strong transverse waves in two-dimensional numerical simulations of cellular detonations is investigated. Resolution studies are performed and it is shown that much higher resolutions than those generally used are required to ensure that the flow and burning structures are well resolved. Resolutions of less than about 20 numerical points in the characteristic reaction length of the underlying steady detonation give very poor predictions of the shock configurations and burning, with the solution quickly worsening as the resolution drops. It is very difficult and dangerous to attempt to identify the physical structure, evolution and effect on the burning of the transverse waves using such under-resolved calculations. The process of transverse wave and triple point collision and reflection is then examined in a very high-resolution simulation. During the reflection, the slip line and interior triple point associated with the double Mach configuration of strong transverse waves become detached from the front and recede from it, producing a pocket of unburnt gas. The interaction of a forward facing jet of exploding gas with the emerging Mach stem produces a new double Mach configuration. The formation of this new Mach configuration is very similar to that of double Mach reflection of an inert shock wave reflecting from a wedge.

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