Homogeneous Grid Research Articles

An estimation of a passive scalar variances using a one-particle Lagrangian transport and diffusion model

In this work the Lagrangian particle diffusion model (LPDM) is extended to include variances and covariances between different passive scalars. This is done by introducing an additional particle variable—the conditional average scalar concentration (CASC) over the particle’s trajectory. In contrast to the particle’s scalar concentration which is conserved, the CASC evolves in time. The model for the evolution equation is compatible with the Eulerian equation for the scalar variance and with the asymptotic behaviour of the particles’ pair probability function.The model calculations are compared with the wind tunnel observations in the neutral boundary layer (Fackrell & Robins (1982) [22]), and with the measurements in decaying homogeneous grid turbulence (Warhaft (1984) [18]). Good agreement is obtained between observations and model predictions. The model is simple to use and can be applied to non-homogeneous turbulence.

Dynamic Energy Aware Gur Game based Algorithms for Self Optimizing Wireless Sensor Networks

This paper presents, Application of Gur Game Based Algorithm on Wireless Sensor Networks (WSNs) deployed to monitor Homogenous and Heterogeneous Grid in order to achieve Quality of Service (QoS) = 0.40 and 0.50. Further, the objectives of all these algorithms are to maximize the coverage of the sensor area while conserving energy consumed by sensor nodes. This is achieved via carefully activating/deactivating the sensors while maximizing the coverage area.

Flow over Hills: A Large-Eddy Simulation of the Bolund Case

Simulation of local atmospheric flows around complex topography is important for several applications in wind energy (short-term wind forecasting and turbine siting and control), local weather prediction in mountainous regions and avalanche risk assessment. However, atmospheric simulation around steep mountain topography remains challenging, and a number of different approaches are used to represent such topography in numerical models. The immersed boundary method (IBM) is particularly well-suited for efficient and numerically stable simulation of flow around steep terrain. It uses a homogenous grid and permits a fast meshing of the topography. Here, we use the IBM in conjunction with a large-eddy simulation (LES) and test it against two unique datasets. In the first comparison, the LES is used to reproduce experimental results from a wind-tunnel study of a smooth three-dimensional hill. In the second comparison, we simulate the wind field around the Bolund Hill, Denmark, and make direct comparisons with field measurements. Both cases show good agreement between the simulation results and the experimental data, with the largest disagreement observed near the surface. The source of error is investigated by performing additional simulations with a variety of spatial resolutions and surface roughness properties.

Climate change impacts on regional winter wheat production in main wheat production regions of China

Wheat is the second primary crop in China. Wheat production in China is an important component for national food security. The combination of high-resolution Global Climate Model (GCM) and WheatGrow model was used to assess the effects of climate change on wheat yields in the main wheat production regions of China. With the application of many techniques including the downscaling of meteorological data, rasterizing of sowing date, parameterization of region cultivar and vectorization of soil data, the spatial data in study area is divided into homogeneous grids with the resolution of 0.1°×0.1°. The grid is taken as the basic simulation unit, and each grid has a complete set of input data (meteorological, soil, management and varieties). Regional productivities are simulated with WheatGrow for each grid cell under scenarios of climate-change. There is an advance in flowering date in future climate compare to 2000s, but with a more homogeneous pattern for the whole producing region. The changes in grain filling period are relatively stable. Under rain-fed conditions, wheat yield is reduced in the north regions of China in three future periods, while wheat yield increases in the south regions of China. Under full-irrigation conditions, irrigated wheat yields will increase in almost all regions of whole producing region. The spatial pattern of evapotranspiration change is quite similar to that of yield change under rain-fed and full-irrigation conditions. The correlation between wheat yield and evapotranspiration (ET) increases to 0.96 and 0.51 (p<0.01) under rain-fed and full-irrigation conditions, respectively. The irrigation water use efficiency (IWUE) will decrease under three time slices in 2030s, 2050s and 2070s in western Shandong, southern Sichuan, as well as northern Henan, Shanxi and Shaanxi, while IWUE will increase under scenarios of climate-change in other areas. The results revealed that the increase in effective irrigation in the future would help to increase the ET and further improve the wheat yield in the northern regions of China, and the limited water should be mad full use of in the regions with relatively high IWUE under scenarios of climate-change.

Semi-transparent silver electrodes for flexible electronic devices prepared by nanoimprint lithography

The preparation of mechanically flexible and optically transparent electronic circuits plays a key role in the development of next-generation display technologies. Silver nano-gratings are of particular interest due to their excellent conductivity and adjustable transmittance. Printed on polymeric substrates they are suitable for an application in flexible opto-electronic devices. Here, we present the preparation of a smart silver precursor system combining both the ability of cheap and scalable nanoimprint patterning and simple thermal silver reduction. Homogeneous silver line and grid patterns with line widths down to 400 nm are prepared using poly(dimethylsiloxane) stamps in a thermal nanoimprint lithography process. Relatively low process temperatures allow the film formation on polymeric substrates. Semi-transparent silver electrodes with a resistance of 2.8 ohm are patterned on polyimide foils to prepare flexible electro-luminescence devices. A detailed investigation of the precursor's thermal decomposition behaviour as well as the resulting electrical and optical properties of the films is offered.

HerschelCHESS discovery of the fossil cloud that gave birth to the Trapezium and Orion KL

As part of the Herschel Guaranteed Time Key Programme CHESS, we present the discovery of a diffuse gas component in the foreground of the intermediate-mass protostar OMC-2 FIR 4, located in the Orion A region. Making use of the full HIFI spectrum of OMC-2 FIR 4 obtained in CHESS, we detected several ground-state lines from OH+, H2O+, HF, and CH+, all of them seen in absorption against the dust continuum emission of the protostar's envelope. The lines peak at a velocity of 9 km/s, which is blue-shifted by 2 km/s with respect to the systemic velocity of OMC-2 FIR 4 (V = 11.4 km/s). We derived column densities for each species, as well as an upper limit to the column density of the undetected H3O+. In order to model and characterise the foreground cloud, we used the Meudon PDR code to run a homogeneous grid of models that spans a reasonable range of densities, visual extinctions, cosmic ray ionisation rates and far-ultraviolet (FUV) radiation fields. The results of our modelling indicate that the foreground cloud is composed of predominantly neutral diffuse gas (n(H) = 100 cm-3) and is heavily irradiated by an external source of FUV that most likely arises from the nearby Trapezium OB association. The cloud is 6 pc thick and bears many similarities with the so-called C+ interface between Orion-KL and the Trapezium cluster, 2 pc south of OMC-2 FIR 4. We conclude that the foreground cloud we detected is an extension of the C+ interface seen in the direction of Orion KL, and interpret it to be the remains of the parental cloud of OMC-1, which extends from OMC-1 up to OMC-2.

Hemilarynx experiments: Statistical analysis of vibrational parameters over changing glottal conditions

In vitro (humans, animals) or in vivo (animals) hemilarynx experiments are still the only way to visualize and analyze 3-D vibrations of the entire medial surface of the vocal fold. However, to date, only a few studies have been performed. For three different larynges during sustained phonation, vibrational output was statistically analyzed as a function of glottal airflow (800 to 1800 ml/s), adductory forces (10, 50, 100 g), and two different anterior–posterior pre-stress conditions (10, 50 g). Using a homogeneous grid of 30 microsutures sewn along the medial surface of the vocal fold, global parameters (empirical eigenfunctions/EEF, f0, subglottal pressure, and sound intensity level) were computed. Similarly, local parameters (displacements, velocities, and accelerations) were analyzed at the 30 different suture locations. The recordings were obtained using a digital high-speed camera (2000 and 4000 fps). Increased airflow resulted in significant statistical changes in all parameter values except the empirical eigenfunctions. For increased adduction and a lower pre-stress (10 g), the local parameters increased more than for the higher pre-stress condition (50 g). For the two pre-stress conditions and an increased adductional force, most global parameters exhibited significant changes (f0, sound intensity, EEF2), while other global parameters (subglottal pressure) did not.

The minimum energy decay rate in quasi-isotropic grid turbulence

We consider high Reynolds number, freely-decaying, isotropic turbulence in which the large scales evolve in a self-similar manner when normalized by the integral scales, u and ℓ. As it is well known, a range of possible behaviors may be observed depending on the form of the longitudinal velocity correlation at large separation, u2f∞=u2f(r→∞). We consider the cases u2f∞=cmr-m,2≤m≤6, whose spectral counterpart is E(k→0)~cmkm-1 for m&amp;lt;6, with or without a lnk correction, and E(k→0)~Ik4 for m=6. (I is Loitsyansky’s integral.) It has long been known that the cm are invariants for m&amp;lt;6, which demands u2ℓm=constant during the decay. This, in turn, sets the energy decay rate as u2~t-(1-p)2m/(m+2), where p is the power-law exponent for the normalized dissipation rate, ɛℓ/ɛℓu3u3~t-p, observed empirically to be a small positive number in grid turbulence. We systematically explore the properties of these different classes of turbulence and arrive at the following conclusions. (i) The invariance of cm is a direct consequence of linear momentum conservation for m≤4, and angular momentum conservation for m=5. (ii) The classical spectra of Saffman, E(k→0)~c3k2, and Batchelor, E(k→0)~Ik4, are robust in the sense that they emerge from a broad class of initial conditions. In particular, it is necessary only that 〈ωiω'j〉∞≤O(r-8) at t=0. The non-classical spectra (m=2,4,5), on the other hand, require very specific initial conditions in order to be realized, of the form 〈ωiω'j〉∞=O(r-(m+2)). (Note the equality rather than the inequality here.) This makes the non-classical spectra less likely to be observed in practice. (iii) The case of m=2, which is usually associated with the u2~t-1 decay law, is pathological in a number of respects. For example, its spectral tensor diverges as k→0, and the long-range correlations 〈uiu'j〉∞=O(r-2) are too strong to be a consequence of the Biot-Savart law. (It is the Biot-Savart law that lies behind the long-range correlations in the classical spectra.) This suggests that m=2 spectra are unlikely to manifest themselves in grid turbulence. A detailed review of the available experimental data is consistent with this assertion. We conclude, therefore, that the minimum energy decay rate in homogeneous grid turbulence is most probably that of Saffman turbulence.

Catching the local

This paper attempts to conceptualize the local neither in exclusive relation to the global nor as a specifically spatial phenomenon but in terms of ethical life, as a conjunction of activities and their consequences. In this sense the local is singular rather than merely a specific site on a homogeneous grid and as much temporal as spatial. The argument is developed with respect to changing meanings of the local in my own ethnographic practice as well as the changes in my main field site in Mayotte, Western Indian Ocean. The depiction of activities draws from and develops the conceptual scheme of Hannah Arendt.

Process-based distributed modeling approach for analysis of sediment dynamics in a river basin

Abstract. Modeling of sediment dynamics for developing best management practices of reducing soil erosion and of sediment control has become essential for sustainable management of watersheds. Precise estimation of sediment dynamics is very important since soils are a major component of enormous environmental processes and sediment transport controls lake and river pollution extensively. Different hydrological processes govern sediment dynamics in a river basin, which are highly variable in spatial and temporal scales. This paper presents a process-based distributed modeling approach for analysis of sediment dynamics at river basin scale by integrating sediment processes (soil erosion, sediment transport and deposition) with an existing process-based distributed hydrological model. In this modeling approach, the watershed is divided into an array of homogeneous grids to capture the catchment spatial heterogeneity. Hillslope and river sediment dynamic processes have been modeled separately and linked to each other consistently. Water flow and sediment transport at different land grids and river nodes are modeled using one dimensional kinematic wave approximation of Saint-Venant equations. The mechanics of sediment dynamics are integrated into the model using representative physical equations after a comprehensive review. The model has been tested on river basins in two different hydro climatic areas, the Abukuma River Basin, Japan and Latrobe River Basin, Australia. Sediment transport and deposition are modeled using Govers transport capacity equation. All spatial datasets, such as, Digital Elevation Model (DEM), land use and soil classification data, etc., have been prepared using raster "Geographic Information System (GIS)" tools. The results of relevant statistical checks (Nash-Sutcliffe efficiency and R–squared value) indicate that the model simulates basin hydrology and its associated sediment dynamics reasonably well. This paper presents the model including descriptions of the various components and the results of its application on two case study areas.

Approximation error of the Lagrange reconstructing polynomial

The reconstruction approach [C.W. Shu, High-order weno schemes for convection-dominated problems, SIAM Rev. 51 (1) (2009) 82–126] for the numerical approximation of f ′ ( x ) is based on the construction of a dual function h ( x ) whose sliding averages over the interval [ x − 1 2 Δ x , x + 1 2 Δ x ] are equal to f ( x ) (assuming a homogeneous grid of cell-size Δ x ). We study the deconvolution problem [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes III, J. Comput. Phys. 71 (1987) 231–303] which relates the Taylor-polynomials of h ( x ) and f ( x ) , and obtain its explicit solution, by introducing rational numbers τ n defined by a recurrence relation, or determined by their generating function, g τ ( x ) , related with the reconstruction pair of e x . We then apply these results to the specific case of Lagrange-interpolation-based polynomial reconstruction, and determine explicitly the approximation error of the Lagrange reconstructing polynomial (whose sliding averages are equal to the Lagrange interpolating polynomial) on an arbitrary stencil defined on a homogeneous grid.

Upscaling Extent vs. Information Loss in Reservoir Upscaling

Upscaling has become an increasingly important tool in recent years for converting highly detailed geological models of a reservoir to simulation grids. The main idea of upscaling is to replace a number of heterogeneous fine grid blocks with one equivalent coarse homogeneous grid block. The common method of upscaling is to replace more than one different value with an effective one. So, the essence of upscaling is averaging. It goes without saying that some information loss in upscaling is inevitable. Studies show that upscaling extent (UE) has a strong positive correlation with information loss. So, in reservoir upscaling, large UE should try to be avoided, especially greater than 0.4.

NAM–SCA: A Nonhydrostatic Anelastic Model with Segmentally Constant Approximations

Abstract An atmospheric convective system may be modeled as an ensemble of discrete plume elements. A representation of decomposited plumes provides the basis for mass-flux convective parameterization. A dry version of such a prototype model is constructed in a two-dimensional horizontally periodic domain. Each discrete plume element is approximated by a horizontally homogeneous segment such that the whole system is given by segmentally constant approximations (SCA) in the horizontal direction for each vertical level in a nonhydrostatic anelastic model (NAM). The distribution of constant segments is highly inhomogeneous in space and evolves with time in a highly adaptive manner. The basic modeling strategy from a physical point of view is to activate new segments vertically upward with time when a convective plume is growing and to deactivate segments when a plume event is over. The difference in physical values crossing segment interfaces is used as a criterion for numerically implementing this strategy. Whenever a large difference is found, the given interface is stretched vertically by subdividing an existing segment into two. In turn, when a segment interface difference is found below the threshold, the given interface is removed, thereby merging the two segments into one. This nonhydrostatic anelastic model with segmentally constant approximations (NAM–SCA) is tested on an idealized atmospheric convective boundary layer. It successfully simulates the evolution of convective plumes with a relatively limited number of segments (i.e., high compression) and with a much scarcer distribution of segments over nonplume environments (i.e., extremely inhomogeneous distribution of segments). Overall, this method compresses the size of the model up to 5 times compared to a standard NAM with homogeneous grid distribution without substantially sacrificing numerical accuracy.

Estimation of Sediment Yield and Areas of Soil Erosion and Deposition for Watershed Prioritization using GIS and Remote Sensing

A Geographical Information System (GIS) based method is proposed and demonstrated for the identification of sediment source and sink areas and the prediction of sediment yield from watersheds. Data from the Haharo sub-catchment having an area of 565 km2 in the Upper Damodar Valley in Jharkhand State in India was taken up for the present study due to availability of gauged data at multiple locations within watershed area. The watershed was discretized into hydrologically homogeneous grid cells to capture the watershed heterogeneity. The cells thus formed were then differentiated into cells of overland flow regions and cells of channel flow regions based on the magnitude of their flow accumulation areas. The gross soil erosion in each cell was calculated using the Universal Soil Loss Equation (USLE). The parameters of the USLE were evaluated using digital elevation model, soil and landuse information on cell basis. The concept of transport limited sediment delivery (TLSD) was formulated and used in ArcGIS for generating the transport capacity maps. An empirical relation is proposed and demonstrated for its usefulness for computation of land vegetation dependent transport capacity factor used in TLSD approach by linking it with normalized difference vegetation index (NDVI) derived from satellite data. Using these maps, the gross soil erosion was routed to the watershed outlet using hydrological drainage paths, for derivation of transport capacity limited sediment outflow maps. These maps depict the amount of sediment rate from a particular grid in spatial domain and the pixel value of the outlet grid indicates the sediment yield at the outlet of the watershed. Up on testing, the proposed method simulated the annual sediment yield with less than ±40% error.

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

Ross [Ross PJ. Modeling soil water and solute transport – fast, simplified numerical solutions. Agron J 2003;95:1352–61] developed a fast, simplified method for solving Richards’ equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988;3:1–15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D.

A comparative analysis of sediment yield simulation by empirical and process-oriented models in Thailand / Une analyse comparative de simulations de l'exportation sédimentaire en Thaïlande à l'aide de modèles empiriques et de processus

Although soil erosion has been recognized worldwide as a threat to the sustainability of natural ecosystems, its quantification presents one of the greatest challenges in natural resources and environmental planning. Precise modelling of soil erosion and sediment yield is particularly difficult, as soil erosion is a highly dynamic process at the spatial scale. The main objective of this study was to simulate soil erosion and sediment yield using two fundamentally different approaches: empirical and process-oriented. The revised form of the Universal Soil Loss Equation (RUSLE), along with a sediment delivery distributed model (SEDD) and the Modified Universal Soil Loss Equation (MUSLE), which are popular empirical models, were applied in a sub-basin of the Mun River basin, Thailand. The results obtained from the RUSLE/SEDD and MUSLE models were compared with those obtained from a process-oriented soil erosion and sediment transport model. The latter method involves spatial disaggregation of the catchment into homogeneous grid cells to capture the catchment heterogeneity. A GIS technique was used for the spatial discretization of the catchment and to derive the physical parameters related to erosion in the grid cells. The simulated outcomes from the process-oriented model were found to be closer to observations as compared to the outcomes of the empirical approaches.

How heterogeneous place cell responding arises from homogeneous grids—A contextual gating hypothesis

How entorhinal grids generate hippocampal place fields remains unknown. The simplest hypothesis-that grids of different scales are added together-cannot explain a number of place field phenomena, such as (1) Summed grids form a repeating, dispersed activation pattern whereas place fields are focal and nonrepeating; (2) Grid cells are active in all environments but place cells only in some, and (3) Partial environmental changes cause either heterogeneous ("partial") remapping in place cells whereas they result in all-or-nothing "realignment" remapping in grid cells. We propose that this dissociation between grid cell and place cell behavior arises in the entorhinal-dentate projection. By our view, the grid-cell/place-cell projection is modulated by context, both organizationally and activationally. Organizationally, we propose that when the animal first enters a new environment, the relatively homogeneous input from the grid cells becomes spatially clustered by Hebbian processes in the dendritic tree so that inputs active in the same context and having overlapping fields come to terminate on the same sub-branches of the tree. Activationally, when the animal re-enters the now-familiar environment, active contextual inputs select (by virtue of their clustered terminations) which parts of the dendritic tree, and therefore which grid cells, drive the granule cell. Assuming this pattern of projections, our model successfully produces focal hippocampal place fields that remap appropriately to contextual changes.

A numerical study of swash flows generated by bores

The dynamic processes of bore propagation over a uniform slope are studied numerically using a 2-D Reynolds Averaged Navier–Stokes (RANS) solver, coupled to a non-linear k − ε turbulence closure and a volume of fluid (VOF) method. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the ‘mini-collapse’ during the runup phase and the ‘back-wash bore’ in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged turbulence kinetic energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate.

Mapping soil erosion susceptibility using remote sensing and GIS: a case of the Upper Nam Wa Watershed, Nan Province, Thailand

Land degradation is still a very common problem in the mountains of Asia because of inappropriate land use practice in steep topography. Many studies have been carried out to map shifting cultivation and areas susceptible to soil erosion. Mostly, estimated soil loss is taken as the basis to classify the level of soil loss susceptibility of area. Factors that influence soil erosion are: rainfall erosivity, soil erodibility, slope length and steepness, crop management and conservation practices. Thus the reliability of estimated soil loss is based on how accurately the different factors were estimated or prepared. As each and every small pixel of our earth surface is different from one area to another, the manner in which the study area was discretized into smaller homogenous sizes and how the most accurate and efficient technique were adopted to estimate the soil loss are very important. The purpose of this study is to produce erosion susceptibility maps for an area that has suffered because of shifting cultivation located in the mountainous regions of Northern Thailand. For this purpose, an integrated approach using RS and GIS-based methods is proposed. Data from the Upper Nam Wa Watershed, a mountainous area of the Northern Thailand were used. An Earth Resources Data Analysis System (ERDAS) imagine image processor has been used for the digital analysis of satellite data and topographical analysis of the contour data for deriving the land use/land cover and the topographical data of the watershed, respectively. ARCInfo and ARCView have been used for carrying out geographical data analysis. The watershed was discretized into hydrologically, topographically, and geographically homogeneous grid cells to capture the watershed heterogeneity. The soil erosion in each cell was calculated using the universal soil loss equation (USLE) by carefully determining its various parameters and classifying the watershed into different levels of soil erosion severity. Results show that during the time of this study most of the areas under shifting cultivation fell in the highest severity class of susceptibility.

A Fourth Order Accurate SH-Wave Staggered Grid Finite-difference Algorithm with Variable Grid Size and VGR-Stress Imaging Technique

This article presents a new approach for the implementation of a planar-free surface boundary condition. It is based on a vertical grid-size reduction above the free surface during the explicit computation of a free surface boundary condition. This technique is very much similar to the well-known stress imaging technique. VGR-stress imaging technique name is proposed for this new free surface boundary condition (VGR stands for ‘vertical grid-size reduction’). To study the performance of the proposed VGR-stress imaging technique, it was implemented in a newly developed second order accurate in time and fourth-order accurate in space (2, 4) staggered grid SH-wave finite-difference (FD) algorithm with variable grid size. It was confirmed that the effective thickness (ETH) of first soil layer becomes less by one-half of vertical grid size than the assigned thickness (ATH), if stress imaging technique is used as a free surface boundary condition. The qualitative and quantitative results of various numerical experiments revealed that the proposed VGR-stress imaging technique is better than the stress imaging technique since it is free from the thickness discrepancy arising due to the use of images of stress components across the free surface. On the basis of iterative numerical experiments, it was confirmed that the stability condition for this FD scheme with variable grid size is $$ \frac{{V_{S} \Delta t}} {{\min (\Delta x,\Delta z)}} \le 0.71. $$ It was also inferred that at least five to six grid points per shortest wavelength are required to avoid the grid dispersion. The maximum grid-spacing ratio up to 12.5 or even more did not affect the accuracy of (2,4) SH-wave algorithm. The obtained reduction of 10.46 and 5.38 folds in the requirement of computational memory and time for a particular basin-edge model, as compared with the homogeneous grid size, reflects the efficacy of the new FD algorithm.