Trapped waves in the neighborhood of a sonic-type singularity

A model equation is derived to study trapped nonlinear waves with a turning effect, occurring in disturbances induced on a two-dimensional steady flow. Only unimodal disturbances under the short wave assumption are considered, when the wave front of the induced disturbance is plane. In the neighbourhood of certain special points of sonic-type singularity, the disturbances are governed by a single first-order partial differential equation in two independent variables. The equation depends on the steady flow through three parameters, which are determined by the variations of velocity and depth, for example (in the case of long surface water waves), along and perpendicular to the wave front. These parameters help us to examine various relative effects. The presence of shocks in a continuously accelerating or decelerating flow has been studied in detail.

Improved prediction of plane transverse jets in supersonic crossflows

THE flowfield due to transverse injection of a round sonic jet into a supersonic flowis a configuration of interest in the design of supersonic combustors or thrust vector control of supersonic jets. The flow is also of fundamental interest because it presents separation from a smooth surface, embedded subsonic regions, curved shear layers, strong shocks, an unusual development of the injected jet into a kidney-shaped streamwise vortex pair, and a wake behind the jet. Although the geometry is simple, the flow is complex and is a good candidate for assessing the behavior of turbulence models for high-speed flow, beginning with the corresponding two-dimensional flow shown in Fig. 1. At the slot, an underexpanded sonic jet expands rapidly into the supersonic crossflow. Expansion waves reflect at the jet boundary, coalesce, and give rise to a Mach surface (Mach disk for round jets).

Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

On shock dynamics

This is in continuation of our paper On the propagation of a multi-dimensional shock of arbitrary strength’ published earlier in this journal (Srinivasan and Prasad [9]). We had shown in our paper that Whitham’s shock dynamics, based on intuitive arguments, cannot be relied on for flows other than those involving weak shocks and that too with uniform flow behind the shock. Whitham [12] refers to this as misinterpretation of his approximation and claims that his theory is not only correct but also provides a natural closure of the open system of the equations of Maslov [3]. The main aim of this note is to refute Whitham’s claim with the help of an example and a numerical integration of a problem in gasdynamics.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

KFVS (Kinetic Flux Vector Splitting) on moving grids for unsteady aerodynamics

Accurate numerical solutions to the problems in fluid-structure (aeroelasticity) interaction are becoming increasingly important in recent years. The methods based on FCD (Fixed Computational Domain) and ALE (Alternate Lagrangian Eulerian) to solve such problems suffer from numerical instability and loss of accuracy. They are not general and can not be extended to the flowsolvers on unstructured meshes. Also, global upwind schemes can not be used in ALE formulation thus leads to the development of flow solvers on moving grids. The KFVS method has been shown to be easily amenable on moving grids required in unsteady aerodynamics. The ability of KFMG (Kinetic Flux vector splitting on Moving Grid) Euler solver in capturing shocks, expansion waves with small and very large pressure ratios and contact discontinuities has been demonstrated.

Modified kinetic flux vector splitting (m-KFVS) method for compressible flows

To resolve many flow features accurately, like accurate capture of suction peak in subsonic flows and crisp shocks in flows with discontinuities, to minimise the loss in stagnation pressure in isentropic flows or even flow separation in viscous flows require an accurate and low dissipative numerical scheme. The first order kinetic flux vector splitting (KFVS) method has been found to be very robust but suffers from the problem of having much more numerical diffusion than required, resulting in inaccurate computation of the above flow features. However, numerical dissipation can be reduced by refining the grid or by using higher order kinetic schemes. In flows with strong shock waves, the higher order schemes require limiters, which reduce the local order of accuracy to first order, resulting in degradation of flow features in many cases. Further, these schemes require more points in the stencil and hence consume more computational time and memory. In this paper, we present a low dissipative modified KFVS (m-KFVS) method which leads to improved splitting of inviscid fluxes. The m-KFVS method captures the above flow features more accurately compared to first order KFVS and the results are comparable to second order accurate KFVS method, by still using the first order stencil. (C) 2011 Elsevier Ltd. All rights reserved.

CFD Based Design Optimizations of the Diffuser of a Gas Dynamically Driver Laser Cavity

Based on the an earlier CFD analysis of the performance of the gas-dynamically controlled laser cavity [1]it was found that there is possibility of optimizing the geometry of the diffuser that can bring about reductions in both size and cost of the system by examining the critical dimensional requirements of the diffuser. Consequently,an extensive CFD analysis has been carried out for a range of diffuser configurations by simulating the supersonic flow through the arrangement including the laser cavity driven by a bank of converging – diverging nozzles and the diffuser. The numerical investigations with 3D-RANS code are carried out to capture the flow patterns through diffusers past the cavity that has multiple supersonic jet interactions with shocks leading to complex flow pattern. Varying length of the diffuser plates is made to be the basic parameter of the study. The analysis reveals that the pressure recovery pattern during the flow through the diffuser from the simulation, being critical for the performance of the laser device shows its dependence on the diffuser length is weaker beyond a critical lower limit and this evaluation of this limit would provide a design guideline for a more efficient system configuration.The observation based on the parametric study shows that the pressure recovery transients in the near vicinity of the cavity is not affected for the reduction in the length of the diffuser plates up to its 10% of the initial size, indicating the design in the first configuration that was tested experimentally has a large factor of margin. The flow stability in the laser cavity is found to be unaffected since a strong and stable shock is located at the leading edge of the diffuser plates while the downstream shock and flow patterns are changed, as one would expect. Results of the study for the different lengths of diffusers in the range of 10% to its full length are presented, keeping the experimentally tested configuration used in the earlier study [1] as the reference length. The conclusions drawn from the analysis is found to be of significance since it provides new design considerations based on the understanding of the intricacies of the flow, allowing for a hardware optimization that can lead to substantial size reduction of the device with no loss of performance.

Community-based Natural Resource Management: Issues and Cases from South Asia

Community-based natural resource management (CBNRM) is the joint management of natural resources by a community based on a community strategy, through a participatory mechanism involving all legitimate stakeholders. The approach is community-based in that the communities managing the resources have the legal rights, the local institutions and the economic incentives to take substantial responsibility for sustained use of these resources. This implies that the community plays an active role in the management of natural resources, not because it asserts sole ownership over them, but because it can claim participation in their management and benefits for practical and technical reasons1–4. This approach emerged as the dominant conservation concept in the late 1970s and early 1980s, of the disillusionment with the developmental state. Governments across South and South East Asia, Africa and Latin America have adopted and implemented CBNRM in various ways, viz. through sectoral programmes such as forestry, irrigation or wildlife management, multisectoral programmes such as watershed development and efforts towards political devolution. In India, the principle of decentralization through ‘gram swaraj’ was introduced by Mahatma Gandhi. The 73rd and 74th constitution amendments in 1992 gave impetus to the decentralized planning at panchayat levels through the creation of a statutory three-level local self-government structure5,6. The strength of this book is that it includes chapters by CBNRM advocates based on six seemingly innovative initiatives being implemented by nongovernmental organizations (NGOs) in ecologically vulnerable regions of South Asia: two in the Himalayas (watershed development programme in Lingmutechhu, Bhuthan and Thalisain tehsil, Paudi Grahwal District, Uttarakhand), three in semi-arid parts of western India (watershed development in Hivre Bazar, Maharashtra and Nathugadh village, Gujarat and water-harvesting structures in Gopalapura, Rajasthan) and one in the flood-plains of the Brahmaputra–Jamuna (Char land, Galibanda and Jamalpur districts, Bangladesh). Watersheds in semi-arid regions fall in the low-rainfall region (500–700 mm) and suffer the vagaries of drought 2–3 years in every five-year cycle. In all these locations, the major occupation is agriculture, most of which is rainfed or dry. The other two cases (in Uttarakhand) fall in the Himalayan region (temperate/sub-temperate climate), which has witnessed extensive deforestation in the last century and is now considered as one of the most vulnerable locations in South Asia. Terraced agriculture is being practised in these locations for a long time. The last case (Gono Chetona) falls in the Brahmaputra–Jamuna charlands which are the most ecologically vulnerable regions in the sub-continent with constantly changing landscape. Agriculture and livestock rearing are the main occupations, and there is substantial seasonal emigration for wage labour by the adult males. River erosion and floods force the people to adopt a semi-migratory lifestyle. The book attempts to analyse the potential as well as limitations of NGOdriven CBNRM endeavours across agroclimatic regions of South Asia with emphasis on four intrinsically linked normative concerns, namely sustainability, livelihood enhancement, equity and demographic decentralization in chapters 2–7. Comparative analysis of these case studies done in chapter 8, highlights the issues that require further research while portraying the strengths and limits of NGO-driven CBNRM. In Hivre Bazar, the post-watershed intervention scenario is such that farmers often grow three crops in a year – kharif bajra, rabi jowar and summer vegetable crops. Productivity has increased in the dry lands due to improvement in soil moisture levels. The revival of johads in Gopalpura has led to the proliferation of wheat and increased productivity. In Lingmuteychhu, productivity gains have also arisen, but more due to the introduction of both local and high-yielding, new varieties as opposed to increased water availability. In the case of Gono Chetona, improvements have come due to diversification of agriculture; for example, the promotion of vegetable gardens. CBNRM interventions in most cases have also led to new avenues of employment and income generation. The synthesis shows that CBNRM efforts have made significant contributions to livelihood enhancement and only limited gains in terms of collective action for sustainable and equitable access to benefits and continuing resource use, and in terms of democratic decentralization, contrary to the objectives of the programme. Livelihood benefits include improvements in availability of livelihood support resources (fuelwood, fodder, drinking water), increased productivity (including diversification of cropping pattern) in agriculture and allied activities, and new sources of livelihood. However, NGO-driven CBNRM has not met its goal of providing ‘alternative’ forms of ‘development’ due to impediments of state policy, short-sighted vision of implementers and confrontation with the socio-ecological reality of the region, which almost always are that of fragmented communities (or communities in flux) with unequal dependence and access to land and other natural resources along with great gender imbalances. Appalling, however, is the general absence of recognition of the importance of and the will to explore practical ways to bring about equitable resource transfer or benefit-sharing and the consequent innovations in this respect that are evident in the pioneering community initiatives such as pani panchayat, etc. Pertaining to the gains on the ecological sustainability front, Hivre Bazar and Thalisain initiatives through active participation of villagers have made significant regeneration of the water table within the village, and mechanisms such as ban on number of bore wells, the regulation of cropping pattern, restrictions on felling of trees and free grazing to ensure that in the future, the groundwater is neither over-exploited nor its recharge capability impaired. Nevertheless, the longterm sustainability of the interventions in the case of Ghoga and Gopalpura initiatives as the focus has been mostly on regeneration of resources, and less on regulating the use of regenerated resources. Further, in Lingmuteychhu and Gono Chetona, the interventions are mainly household-based and the focus has been less explicit on ecological components. The studies demonstrate the livelihood benefits to all of the interventions and significant variation in achievements with reference to sustainability, equity and democratic decentralization depending on the level and extent of community participation apart from the vision of implementers, strategy (or nature of intervention shaped by the question of community formation), the centrality of community formation and also the State policy. Case studies show that the influence of State policy is multi-faceted and often contradictory in nature. This necessitates NGOs to engage with the State in a much more purposeful way than in an ‘autonomous space’. Thus the role of NGOs in CBNRM is complementary, wherein they provide innovative experiments that the State can learn. This helps in achieving the goals of CBNRM through democratic decentralization. The book addresses the vital issues related to natural resource management and interests of the community. Key topics discussed throughout the book are still at the centre of the current debate. This compilation consists of well-written chapters based on rigorous synthesis of CBNRM case studies, which will serve as good references for students, researchers and practitioners in the years to come.

Calculation of the front part of the sonic boom signature for a Maneuvering aerofopil

The sonic boom at a large distance from its source consists of a leading shock, a trailing shock and a one parameter family of nonlinear wavefronts in between these shocks. A new ray theoretical method using a shock ray theory and a weakly nonlinear lay theory has been used to obtain the shock fronts and wavefronts respectively, for a maneuvering aerofoil in a homogeneous medium. This method introduces a one parameter family of Cauchy problems to calculate the shock and wave fronts emerging from the surface of the aerofoil. These problems are solved numerically to obtain the leading shock front and the nonlinear wavefronts emerging from the front portion of the aerofoil.

Optimised form of acceleration correction algorithm within SPH-based simulations of impact mechanics

In the context of SPH-based simulations of impact dynamics, an optimised and automated form of the acceleration correction algorithm (Shaw and Reid, 2009a) is developed so as to remove spurious high frequency oscillations in computed responses whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. A rational framework for an insightful characterisation of the erstwhile acceleration correction method is first set up. This is followed by the proposal of an optimised version of the method, wherein the strength of the correction term in the momentum balance and energy equations is optimised. For the first time, this leads to an automated procedure to arrive at the artificial viscosity term. In particular, this is achieved by taking a spatially varying response-dependent support size for the kernel function through which the correction term is computed. The optimum value of the support size is deduced by minimising the (spatially localised) total variation of the high oscillation in the acceleration term with respect to its (local) mean. The derivation of the method, its advantages over the heuristic method and issues related to its numerical implementation are discussed in detail. (C) 2011 Elsevier Ltd. All rights reserved.

Stabilized SPH-based simulations of impact dynamics using acceleration-corrected artificial viscosity

Artificial viscosity in SPH-based computations of impact dynamics is a numerical artifice that helps stabilize spurious oscillations near the shock fronts and requires certain user-defined parameters. Improper choice of these parameters may lead to spurious entropy generation within the discretized system and make it over-dissipative. This is of particular concern in impact mechanics problems wherein the transient structural response may depend sensitively on the transfer of momentum and kinetic energy due to impact. In order to address this difficulty, an acceleration correction algorithm was proposed in Shaw and Reid (''Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics'', Comput. Methods Appl. Mech. Engrg., 198, 3962-3974) and further rationalized in Shaw et al. (An Optimally Corrected Form of Acceleration Correction Algorithm within SPH-based Simulations of Solid Mechanics, submitted to Comput. Methods Appl. Mech. Engrg). It was shown that the acceleration correction algorithm removes spurious high frequency oscillations in the computed response whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. In this paper, we aim at gathering further insights into the acceleration correction algorithm by further exploring its application to problems related to impact dynamics. The numerical evidence in this work thus establishes that, together with the acceleration correction algorithm, SPH can be used as an accurate and efficient tool in dynamic, inelastic structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

Microearthquake activity near the Idukki Reservoir, south India: A rare example of renewed triggered seismicity

Earthquakes triggered by artificial reservoirs have been documented for more than seven decades and the processes leading to this phenomenon are fairly well understood. Larger among such earthquakes are known to occur within a few years of reservoir impoundment and usually the activity decreases with time. A documented example of Reservoir Triggered Seismicity (RTS), the Idukki Reservoir in Kerala, south India, impounded in 1975, is an exception wherein the triggered activity has been revived in 2011, nearly 35 years after the initial burst of activity in 1977, two years after the dam was filled. The magnitude of the largest shock in the 2011 sequence exceeded that of the previously documented largest microearthquake. Presence of faults that are close to failure and vulnerable to increase in pore pressure due to reservoir loading or increased rainfall, or a combination of both seems to trigger shocks in this area. The renewed burst of earthquakes after a prolonged period of reduced activity at the Idukki Reservoir is a rare example of RTS. (C) 2012 Elsevier B.V. All rights reserved.

Interface capturing simulations of acoustically driven bubble dynamics in and near tissue

Tissue injury during therapeutic ultrasound or lithotripsy is thought, in cases, to be due to the action of cavitation bubbles. Assessing this and mitigating it is challenging since bubble dynamics in the complex confinement of tissues or in small blood vessels are challenging to predict. Simulations tools require specialized algorithms to simultaneously represent strong acoustic waves and shocks, topologically complex liquid‐vapor phase boundaries, and the complex viscoelastic material dynamics of tissue. We discuss advances in a simulation tool for such situations. A single‐mesh Eulerian solver is used to solve the governing equations. Special sharpening terms maintain the liquid‐vapor interface in face of the finite numerical dissipation included in the scheme to accurately capture shocks. A recent enhancement to this formulation has significantly improved this interface capturing procedure, which is demonstrated for simulation of the Rayleigh collapse of a bubble. The solver also transports elastic stresses and can thus be used to assess the effects of elastic properties on bubble dynamics. A shock‐induced bubble collapse adjacent to a model elastic tissue is used to demonstrate this and draw some conclusions regarding the injury suppressing role that tissue elasticity might play.

In a hot bubble: why does superbubble feedback work, but isolated supernovae do not?

Using idealized one-dimensional Eulerian hydrodynamic simulations, we contrast the behaviour of isolated supernovae with the superbubbles driven by multiple, collocated supernovae. Continuous energy injection via successive supernovae exploding within the hot/dilute bubble maintains a strong termination shock. This strong shock keeps the superbubble over-pressured and drives the outer shock well after it becomes radiative. Isolated supernovae, in contrast, with no further energy injection, become radiative quite early (less than or similar to 0.1Myr, tens of pc), and stall at scales less than or similar to 100 pc. We show that isolated supernovae lose almost all of their mechanical energy by 1 Myr, but superbubbles can retain up to similar to 40 per cent of the input energy in the form of mechanical energy over the lifetime of the star cluster (a few tens of Myr). These conclusions hold even in the presence of realistic magnetic fields and thermal conduction. We also compare various methods for implementing supernova feedback in numerical simulations. For various feedback prescriptions, we derive the spatial scale below which the energy needs to be deposited in order for it to couple to the interstellar medium. We show that a steady thermal wind within the superbubble appears only for a large number (greater than or similar to 10(4)) of supernovae. For smaller clusters, we expect multiple internal shocks instead of a smooth, dense thermalized wind.