Asymptotic Formulation

2011 ◽  
pp. 79-86
Author(s):  
A. J. Hermans
Keyword(s):  
Asymptotic Formulation

Wedge-Shaped Shell Structure Impacting a Water Surface

2005 ◽  
Author(s):  
Adrian Constantinescu ◽  
Volker Bertram ◽  
Ion Fuiorea ◽  
Alain Neme
Keyword(s):  
Water Surface ◽  
Surface Velocity ◽  
Convergence Criterion ◽  
Surface Boundary ◽  
Fluid Structure ◽  
Pressure Fields ◽  
Wet Surface ◽  
Peak Pressures ◽  
The Impact ◽  
Asymptotic Formulation

This paper presents a study of fluid structure interaction during the impact of a ship on a water surface. The analysis combines the assumption of small displacements for the ideal fluid and the solid with an asymptotic formulation for accurate pressure evaluation on the wet surface boundary. A fluid-heat analogy is used to obtain the regular displacement, velocity and pressure fields in the fluid domain with ABAQUS/Standard finite element code. PYTHON and FORTRAN languages are also employed to connect fluid and structure data. Two methods are developed. The first method employs a weak fluid-structure coupling. The average discrepancy between our numerical results and experiments was 22% for the peak pressures for conical shell structures. The wet surface velocity was well predicted. The second method (implicit fluid-structure coupling using a convergence criterion) is more accurate. Recent results with an improved, numerical hydrodynamic model based on CFD are also presented.

scholarly journals Linear and weakly nonlinear instability of a premixed curved flame under the influence of its spontaneous acoustic field

2014 ◽  
Vol 758 ◽  
pp. 180-220 ◽  
Author(s):  
Raphaël C. Assier ◽  
Xuesong Wu
Keyword(s):  
Acoustic Field ◽  
Numerical Solutions ◽  
Parametric Instability ◽  
Linear Instability ◽  
Weakly Nonlinear ◽  
Observed Behaviour ◽  
Hydrodynamic Field ◽  
The Stability ◽  
Sivashinsky Equation ◽  
Asymptotic Formulation

AbstractThe stability of premixed flames in a duct is investigated using an asymptotic formulation, which is derived from first principles and based on high-activation-energy and low-Mach-number assumptions (Wu et al., J. Fluid Mech., vol. 497, 2003, pp. 23–53). The present approach takes into account the dynamic coupling between the flame and its spontaneous acoustic field, as well as the interactions between the hydrodynamic field and the flame. The focus is on the fundamental mechanisms of combustion instability. To this end, a linear stability analysis of some steady curved flames is undertaken. These steady flames are known to be stable when the spontaneous acoustic perturbations are ignored. However, we demonstrate that they are actually unstable when the latter effect is included. In order to corroborate this result, and also to provide a relatively simple model guiding active control, we derived an extended Michelson–Sivashinsky equation, which governs the linear and weakly nonlinear evolution of a perturbed flame under the influence of its spontaneous sound. Numerical solutions to the initial-value problem confirm the linear instability result, and show how the flame evolves nonlinearly with time. They also indicate that in certain parameter regimes the spontaneous sound can induce a strong secondary subharmonic parametric instability. This behaviour is explained and justified mathematically by resorting to Floquet theory. Finally we compare our theoretical results with experimental observations, showing that our model captures some of the observed behaviour of propagating flames.

scholarly journals Asymptotic Weyl double copy

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hadi Godazgar ◽  
Mahdi Godazgar ◽  
Ricardo Monteiro ◽  
David Peinador Veiga ◽  
C. N. Pope
Keyword(s):  
Black Holes ◽  
Gauge Transformation ◽  
Single Copy ◽  
Characteristic Value ◽  
Full Solution ◽  
Double Copy ◽  
Asymptotic Formulation ◽  
Large Gauge Transformation ◽  
Asymptotic Symmetries

Abstract A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a large gauge transformation.

scholarly journals Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

2021 ◽  
Vol 15 (1) ◽  
pp. 30-36
Author(s):  
Askar Kudaibergenov ◽  
Askat Kudaibergenov ◽  
Danila Prikazchikov
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Moving Load ◽  
Elastic Half Space ◽  
Elementary Functions ◽  
Material Models ◽  
Line Load ◽  
Transient Regimes ◽  
Surface Wave Field ◽  
Asymptotic Formulation

Abstract The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

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