Development and Application of High-Resolution Adaptive Numerical Techniques in Shock Wave Research Center

Saito, Tsutomu; Voinovich, P. A.; Timofeev, Edward N.; Takayama, K.

doi:10.1007/978-1-4615-0663-8_76

Cited by 22 publications

(6 citation statements)

References 20 publications

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“…Prior to energy release via pressure modification for a source, the grid is refined in the vicinity of the source, regardless of the sensor values in the region, so that the energy release and subsequent induced wave motion would be always resolved on the finest mesh. The data structure and adaptation procedure of the adaptive code were adopted, with suitable simplification, from the 2-D unstructured Euler code described by Saito et al [49] to a 1-D code. Preliminary numerical trials demonstrated that simple linear solution interpolation used in the code [49] when inserting a new node led to significant (of the order of 5%) error in wave speeds when long distance propagation typical for the problem under consideration was simulated.…”

Section: Methodsmentioning

confidence: 99%

Effect of spatial discretization of energy on detonation wave propagation

Timofeev

Higgins

2017

J. Fluid Mech.

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Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are now embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the lab-fixed reference frame. Two different solvers are used: one with a fixed uniform grid and the other using an unstructured, adaptively refined grid enabling the limit of highly concentrated, spatially discrete sources to be examined. The two different solvers generate consistent results, agreeing within the accuracy of the measured wave speeds. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. The effect of source delay time, source energy density, specific heat ratio, and the spatial discreteness of the sources on the wave speed is studied. Sources fixed in the lab reference frame versus sources that convect with the flow are compared as well. The average wave speed is compared to the ideal Chapman-Jouguet (CJ) speed of the equivalent homogenized media. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as great as 15%. The deviation above the CJ value increases with decreasing values of specific heat ratio γ. The total energy release, delay time, and whether the sources remain lab-fixed or are convected with the flow do not have a significant influence on the deviation of the average wave speed away from CJ. A simple, ad hoc analytic model is proposed to treat the case of zero delay time (i.e., source energy released at the shock front) that exhibits qualitative agreement with the computational solutions and may explain why the deviation from CJ increases with decreasing γ. When the sources are sufficiently spread out so as to make the energy release of the media nearly continuous, the classic CJ solution is obtained for the average wave speed. Such continuous waves can also be shown to have a time-averaged structure consistent with the classical ZND structure of a detonation. In the limit of highly discrete sources, temporal averaging of the wave structure shows that the effective sonic surface does not correspond to an equilibrium state. The average state of the flow leaving the wave in this case does eventually reach the equilibrium Hugoniot, but only after the effective sonic surface has been crossed. Thus, the super-CJ waves observed in the limit of highly discretized sources can be understood as weak detonations due to the...

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Section: Methodsmentioning

confidence: 99%

Effect of spatial discretization of energy on detonation wave propagation

Timofeev

Higgins

2017

J. Fluid Mech.

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“…The finite-volume code is based on a triangular unstructured grid with control volumes being constructed around each node. The respective formulas may be found in [14,16] and very closely resemble (76), (78), with the summation of fluxes for all faces (in 1D cases we have just two faces). In the original code an exact Riemann solver is used to compute fluxes at each face from the "left" and "right" values.…”

Section: Second-order and Multidimensional Extensionsmentioning

confidence: 94%

“…First, we mention here the studies of shock wave propagation in water assuming that the Tait equation of state is valid and employing the locally adaptive unstructured 2D and 3D codes [14]. In fact, almost the same formulas as those for perfect gases can be used in this case.…”

Section: Brief Review Of Applicationsmentioning

confidence: 99%

“…The technique has some attractive features, being accurate and rather robust, with a simple predictor step without any Riemann solvers, which contributes to efficiency, and easily applicable to any kind of grid, structured or unstructured alike. In fact, we have used it quite extensively in various applications during the last decade (see [14]). …”

Section: Second-order and Multidimensional Extensionsmentioning

confidence: 99%

See 1 more Smart Citation

Artificial Wind—A New Framework to Construct Simple and Efficient Upwind Shock-Capturing Schemes

Соколов¹,

Timofeev²,

Sakai

et al. 2002

Journal of Computational Physics

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“…11 Both codes feature essentially the same numerical methods conceptually similar to the MUSCL-Hancock method. 12,13 Unstructured grids with triangular and tetrahedral elements are used to discretize 2D/axisymmetric and 3D computational domains, respectively. Both codes employ local grid adaptation via the classical h-refinement to achieve high resolution of localized flow features (e.g., discontinuities) at low computational cost.…”

Section: Numerical Modelmentioning

confidence: 99%

Startability analysis of Busemann intakes with overboard spillage

Moradian

Timofeev

Tahir³

et al. 2014

19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference

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In this work quasi-steady starting of Busemann intakes with overboard mass spillage is considered analytically and simulated numerically using 2D and 3D unstructured adaptive Euler finite-volume flow solvers. Two designs of Busemann intakes are under consideration: the conventional one based on Busemann flow with a weak conical shock and a newly proposed one based on Busemann flow with a strong conical shock. For both designs, the overboard spillage is achieved by cutting out an angular section of the full Busemann intake and covering the cuts with flat plates allowing for overboard spillage and maintaining the Busemann flow in the started mode. The theory predicting the self-starting (spontaneous starting) area ratios for Busemann intakes with overboard spillage is outlined. Methodology of finding the self-starting area ratios for a given free-stream Mach number via numerical experiments is discussed and applied to Busemann intakes with different capture angles. The numerical findings confirm the theoretical predictions of self-starting boundaries. It is demonstrated that overboard spillage significantly improves the starting characteristics of Busemann intakes. Furthermore, the strong-shock design leads to markedly better starting characteristics.

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Development and Application of High-Resolution Adaptive Numerical Techniques in Shock Wave Research Center

Cited by 22 publications

References 20 publications

Effect of spatial discretization of energy on detonation wave propagation

Effect of spatial discretization of energy on detonation wave propagation

Artificial Wind—A New Framework to Construct Simple and Efficient Upwind Shock-Capturing Schemes

Startability analysis of Busemann intakes with overboard spillage

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