Fine Grid Size Research Articles

Blood flow dynamics in patient-specific cerebral aneurysm models: The relationship between wall shear stress and aneurysm area index

Hemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The temporal and spatial variations in wall shear stress (WSS) within the aneurysmal sac are hypothesized to be correlated with the growth and rupture of the aneurysm. The current work describes the blood flow dynamics in 34 patient-specific models of saccular aneurysms located in the region of the anterior and posterior circulation of the circle of Willis. The models were obtained from three-dimensional rotational angiography image data and blood flow dynamics was studied under a physiologically representative waveform of inflow. The three-dimensional continuity and momentum equations for unsteady laminar flow were solved with commercial software using non-structured fine grid sizes. The vortex structure, the wall pressure, and the WSS showed large variations, depending on the morphology of the artery, size of the aneurysm, and form. A correlation existed between the mean WSS on the aneurysmal sac for lateral unruptured and ruptured aneurysms with an aneurysm surface index, which is defined as the ratio between the aneurysm area and the artery area at model inlet, respectively.

SU‐FF‐T‐14: A High MU Efficiency Dynamic MLC Leaf Sequencing Algorithm

Purpose: MU efficiency is a major figure of merit for dMLC leaf sequencing. However, leaf sequencing is often generated with focus on other constraints and the MU efficiency is taken as a byproduct. This work is to develop a new dMLC leaf sequencing algorithm (MinMU) that explicitly minimize the total MU. Method & Materials: At a constant dose rate, the maximum MU efficiency is achieved by minimizing, through optimization, an objective function which is essentially the total beam on time. The constraints considered are: maximum leaf speed, maximum separation between leaves and under dosing caused by tongue‐and‐groove effect. These mixed integer constraints are converted to linear ones by enumerating and eliminating redundant scenarios, for a given intensity map. These steps also help eliminating the infeasible solutions. The optimization was implemented for the Varian Millenium 120‐leaf MLC and was solved with the CPLEX software. Its performance was tested against published algorithms using phantom and real patient treatment fluence maps. Results: The fluence maps in the phantom study were generated with various grid sizes. The MU increases at a much slower rate for the MinMU algorithm than for the published algorithms with finer grid size. The MU efficiency advantage of the MinMU is more pronounced for more complex and larger fluences.Among the 18 fluence maps that were taken from two real head‐and‐neck cancer treatment plans, the MinMU algoithm uses more MU for 2 fluence maps, same MU for 2, and less MU for the rest 14 fluence maps than the commercial treatment planning software. Overall, the MinMU used 10% and 7% less MU for the two plans, respectively. Also, the MinMU reproduced the original optimal fluence with minimal difference. Conclusion: A new dMLC leaf sequencing algorithm is developed. Its high MU efficiency potential is demonstrated.

Numerical simulation of tethered buoy dynamics using mixed finite elements

In this article, we devise a simulation tool of the dynamics of a tethered buoy, which is a mooring system consisting of a rigid floating body (buoy) connected by an elastic cable (mooring line) to the bottom of the fluid environment. The accuracy and robustness of the overall solution algorithm are based on an appropriate choice of three main ingredients. The first ingredient is the use of a novel mixed finite element formulation for the mooring line, which allows a robust modeling of the cable even in the limit of an infinite value of the Young modulus. The second ingredient is the use of quaternions in the equations of motion of the floating body, instead of Euler angles, which avoids angle singularities in the presence of large rotations. The third ingredient is the use of an implicit method (Backward Euler) for time discretization, in conjunction with a damped Newton method for the solution of the resulting nonlinear system, which avoids computational inefficiency of explicit time integration schemes in the presence of quasi-inextensible cables and a fine spatial grid size. The physical soundness of the mooring system model and the accuracy and robustness of the proposed numerical procedure are validated in the study of a tethered buoy operating under static and dynamic industrial-like working conditions.

Comparison of haemodynamics in cerebral aneurysms of different sizes located in the ophthalmic artery

AbstractHaemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The temporal and spatial variations of the wall shear stress in the aneurysmal sac are hypothesized to be correlated with its growth and rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This work describes the flow dynamics in patient‐specific models of saccular aneurysms of different sizes located in the ophthalmic artery. The models were obtained from three‐dimensional rotational angiography image data and blood flow dynamics was studied under physiologically representative waveform of inflow. The three‐dimensional continuity and momentum equations for unsteady laminar flow were solved with commercial software using nonstructured fine grid sizes. The intra‐aneurysmal flows show complex vortex structures that change during one pulsatile cycle. A relation between the aneurysm aspect ratio and the mean wall shear stress on the aneurysmal sac is showed. Copyright © 2006 John Wiley & Sons, Ltd.

NUMERICAL STUDY ON THE SEAWALL'S EFFECT AGAINST TSUNAMI RUN-UP AT MALE' ISLAND

Male' Island, the capital of Maldives, was hit by Indian Ocean Tsunami on December 26 2004, but the damage was less severe in comparison with other islands in Maldives and neighbor countries. One of the major reasons was attributed to the solid seawalls surrounding the island. In this study, the effects of the seawalls were inspected by numerical simulation, in which the finest grid size was 3.33m for the whole Male' Island. The results indicated that Male' Island without seawalls would have been hit by run-up flows with higher energy several times, especially on the east coast facing to the tsunami source. Thus it is certain that the existing seawalls reduced the damage of Male' Island as long as this event. In fact, the maximum tsunami height in Maldives, however, was relatively small, approx. 2m, so that the existing seawalls worked well against the tsunami. So it may be needed to implement other software methods; forecast and alert system, evacuation guideline system etc., as well as shore protection structures in preparation for larger scale tsunamis.

A numerical study of turbulent mixing in eruption clouds using a three‐dimensional fluid dynamics model

The dynamics of eruption clouds in explosive volcanic eruptions are governed by entrainment of ambient air into eruption clouds by turbulent mixing. We develop a new numerical pseudo gas model of an eruption cloud by employing three‐dimensional coordinates, a third‐order accuracy scheme, and a fine grid size in order to investigate the behavior of entrainment due to turbulent mixing. The quantitative features of entrainment are measured by a proportionality constant relating the inflow velocity at the edge of the flow to the average vertical velocity (i.e., the entrainment coefficient). Our model has successfully reproduced the quantitative features of entrainment observed in the laboratory experiments as well as fundamental features of the dynamics of eruption clouds, such as the generation of eruption columns and/or pyroclastic flows. The value of the entrainment coefficient for eruption clouds is estimated from the column height and critical condition for column collapse by comparing results of our model with those of previous one‐dimensional models. It is suggested that the value of the entrainment coefficient for an eruption cloud is approximately constant, although the value estimated from the critical condition for column collapse (k ∼ 0.07) is slightly smaller than that based on the column height (k ∼ 0.1). This difference reflects the vertical change of flow structure in the eruption cloud. The eruption cloud in the upper region exhibits a meandering instability, which leads to efficient mixing, whereas the cloud near the vent maintains a concentric structure with an inner dense core surrounded by an outer shear region. Our model is consistent with previous one‐dimensional models for steady eruption clouds supported by the laboratory experiments, and it is also applicable to unsteady and transient features of actual eruption clouds.

DEM resolution effects on shallow landslide hazard and soil redistribution modelling

AbstractIn this paper we analyse the effects of digital elevation model (DEM) resolution on the results of a model that simulates spatially explicit relative shallow landslide hazard and soil redistribution patterns and quantities. We analyse distributions of slope, specific catchment area and relative hazard for shallow landsliding for four different DEM resolutions (grid sizes of 10, 25, 50 and 100 m) of a 12 km2 study area in northern New Zealand. The effect of DEM resolution is especially pronounced for the boundary conditions determining a valid hazard calculation. For coarse resolutions, the smoothing effect results in a larger area becoming classified as unconditionally stable or unstable. We apply simple empirical soil redistribution algorithms for scenarios in which all sites with a certain landslide hazard fail and generate debris flow. The lower initial number of failing cells but also the inclusion of slope (limit) in those algorithms becomes apparent with coarser resolutions. For finer resolutions, much larger amounts of soil redistribution are found, which is attributed to the more detailed landscape representation. Looking at spatial patterns of landslide erosion and sedimentation, the size of the area affected by these processes also increases with finer resolutions. In general, landslide erosion occupies larger parts of the area than deposition, although the total amounts of soil material eroded and deposited are the same. Analysis of feedback mechanisms between soil failures over time shows that finer resolutions show higher percentages of the area with an increased or decreased landslide hazard. When the extent of sites with lower and higher hazards are compared, finer grid sizes and higher landslide hazard threshold scenarios tend to increase the total extent of areas becoming more stable relative to the less stable ones. Extreme care should be taken when quantifying landslide basin sediment yield by applying simple soil redistribution formulas to DEMs with different resolutions. Rather, quantities should be interpreted as relative amounts. For studying shallow landsliding over a longer timeframe, the ‘perfect’ DEM resolution may not exist, because no resolution can possibly represent the dimensions of all different slope failures scattered in space and time. We assert that the choice of DEM resolution, possibly restricted by data availability in the first place, should always be adapted to the context of a particular type of analysis. Copyright © 2005 John Wiley & Sons, Ltd.

Slow shock interactions in the heliosphere using an adaptive grid MHD model

Abstract. A one-dimensional (1-D), time-dependent, adaptive-grid MHD model with solar wind structure has been used in the past to study the interaction of shocks. In the present study, we wish to study some fundamental processes that may be associated with slow shock genesis and their possible interactions with other discontinuities. This adaptive-grid model, suitable for appropriate spatial and temporal numerical simulations, is used for this purpose because its finer grid sizes in the vicinity of the steep gradients at shocks make it possible to delineate the physical parameters on both sides of the shocks. We found that a perturbation with deceleration of solar wind will generate an ensemble consisting of a forward slow shock, a fast forward wave and a reverse slow shock. On the other hand, a perturbation with an increase in acceleration of solar wind will generate both a slow shock and a fast shock. These two perturbations, although not unique, may be representative of momentum and pressure changes at the solar surface. During the transition of a fast shock overtaking a slow shock from behind, the slow shock might disappear temporarily. Also, during the process of the merging of two slow shocks, a slow shock-like structure is formed first; later, the slow shock-like structure evolves into an intermediate shock-like structure. This intermediate shock-like structure then evolves into an intermediate wave and a slow shock-like structure. Finally, the slow shock-like structure evolves into a slow shock, but the intermediate wave disappears by interacting with the non-uniform solar wind. This complex behavior demonstrates the non-unique nature of the formation of slow shocks, intermediate shocks and their derivative structures. We emphasize the main aim of this work to be both: (a) non-unique input physical parameters to explain the paucity of observed slow shocks, as well as (b) the impossibility of backward tracing to the history of input boundary conditions in view of the present inability to describe unambiguous inputs at the Sun.

An eddy-permitting oceanic general circulation model and its preliminary evaluation

An eddy-permitting, quasi-global oceanic general circulation model, LICOM (LASG/IAP (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics) Climate System Ocean Model), with a uniform grid of 0.5° × 0.5° is established. Forced by wind stresses from Hellerman and Rosenstain (1983), a 40-yr integration is conducted with sea surface temperature and salinity being restored to the Levitus 94 datasets. The evaluation of the annual mean climatology of the LICOM control run shows that the large-scale circulation can be well reproduced. A comparison between the LICOM control run and a parallel integration of L30T63, which has the same framework but a coarse resolution, is also made to confirm the impact of resolution on the model performance. On account of the reduction of horizontal viscosity with the enhancement of the horizontal resolution, LICOM improves the simulation with respect to not only the intensity of the large scale circulations, but also the magnitude and structure of the Equatorial Undercurrent and South Equatorial Current. Taking advantage of the fine grid size, the pathway of the Indonesian Throughflow (ITF) is better represented in LICOM than in L30T63. The transport of ITF in LICOM is more convergent in the upper layer. As a consequence, the Indian Ocean tends to get warmer in LICOM. The poleward heat transports for both the global and individual basins are also significantly improved in LICOM. A decomposed analysis indicates that the transport due to the barotropic gyre, which primarily stands for the barotropic effect of the western boundary currents, plays a crucial role in making the difference.

The cellular structure of a two-dimensional H2/O2/Ar detonation wave

In this paper, the cellular structure of a two-dimensional detonation wave in a low pressure H2/O2/Ar mixture calculated with a detailed chemical reaction model, high order scheme and high resolution grids is investigated. The regular cellular structure is produced about 1 ms after introducing perturbations in the reaction zone of a steady one-dimensional detonation wave. It is found from the present resolution study that the discrepancies concerning the structure type arising from the coarser grid employed can be resolved using a sufficiently fine grid size of 0.05 mm and below and shows a double-Mach-like strong-type configuration. During the structure evolution process, the structure configuration does not change much in the periods before and after the triple point collision. Through the triple point collision, three regular collision processes are observed and are followed by a quick change to the double-Mach-like configuration. The simulated structure tracks show that there are three different tracks associated with different triple points or the kink on the transverse wave. Comparisons with previous work and experiments indicate the presence of a strong structure for an ordinary detonation.

Subparallel dipping heterogeneities in the mid‐lower mantle

Data from western U.S. short‐period seismic networks show anomalous later phases which we interpret as S‐to‐P converted waves from heterogeneities in the mid‐lower mantle (depths of ∼1000–1850 km) northeast of the Mariana subduction zone. The geometry of the objects is mapped by a two‐step approach: (1) computing the S‐to‐P scattering likelihood with the arrival time, slowness, and azimuth of the later arrivals measured by array techniques relative to direct P waves, and (2) by direct use of the waveforms using semblance. At least three subparallel objects are detected in the lower mantle study region, with the dips of 30° to 40° southward and with a lateral extent larger than 500 km by 300 km. The elastic properties associated with the heterogeneous objects appear to change within several kilometers, considering their high efficiency at converting short‐period waves (wavelengths of 5–10 km). Previous seismic tomography studies have not predicted significant velocity anomalies around the heterogeneities. This is probably because they are below the resolution limit of present methods. The three major heterogeneities are separated from each other nearly 300 km vertically, and significant anomalies seem absent between each object. Nevertheless, semblance cross sections with a finer grid size (0.1° × 0.1° × 10 km) of the clearest intermediate object (at 1400–1600 km) show a hint that the object is not a single interface but is actually composed of double interfaces nearly 50 km apart. Purely thermal anomalies of kilometers scale must be transient features in the mantle and thus are highly unlikely to be the cause of the heterogeneities. They should rather represent either sharp chemical variations in major element composition or sharp changes in preferred orientations of anisotropic lattice of the lower mantle minerals. Thermal anomalies, however, may be superimposed on such variations because of heat generation either by concentrated radioactive nuclei or by viscous shear heating due to deformations. A plausible tectonic interpretation of these dipping objects is that they represent remnants of subducted lithospheric plates which preceded the current subduction of the Pacific plate. Although we cannot make conclusive arguments on what the mechanism of creating such heterogeneities from these observations alone, we suggest that they may represent stretched, thinned, and duplexed rocks within chaotic mantle flows.

Numerical Study of the Intertropical Convergence Zone Over the Indian Ocean During the 1997 and 1998 Northeast Monsoon Episodes

— The hydrostatic Naval Research Laboratory/North Carolina State University (NRL/NCSU) model was used to study the mesoscale dynamics and diurnal variability of the Intertropical Convergence Zone (ITCZ) over the Indian Ocean in the short-range period. To achieve this objective the initial conditions from two northeast monsoon episodes (29 January, 1997 and 29 January, 1998) were run for 48-hour simulations using a triple-nested grid version of the model with 1.5° × 1.5°, 0.5° × 0.5° and 0.17° × 0.17° resolutions. The 1997 case represents a typical northeast monsoon episode, while the 1998 case depicts an abnormal monsoon episode during an El Nino event.¶Comparisons between the model-produced and analyzed mean circulation, wind speed, and associated rainfall for different spatial scales are presented. During the active northeast monsoon season in 1997, the major low-level westerly winds and associated high rainfall rates between 0° and 15°S were simulated reasonably well up to 24 hours. During the 1998 El Nino event, the model was capable of simulating weak anomalous easterly winds (between 0° and 15°S) with much lower rainfall rates up to 48 hours. In both simulations, the finest grid size resulted in largest rainfall rates consistent with Outgoing Longwave Radiation data.¶The model performance was further evaluated using the vertical profiles of the vertical velocity, the specific humidity and temperature differences between the model outputs and the analyses. It is found that during a typical northeast monsoon year, 1997, the water vapor content in the middle troposphere was largely controlled by the low-level convergence determined by strong oceanic heat flux gradient. In contrast, during the 1998 El Nino year moisture was present only in the lower troposphere. Due to strong subsidence associated with Walker circulation over the central and eastern Indian Ocean, deep convection was not present. Finally, the diurnal variations of the maximum rainfall, vertical velocity and total heat flux were noticeable only during the 1997 northeast monsoon year.

Application of the nested grid STEM to an early summer acid rain in South Korea

The nested grid Sulfur Transport Eulerian Model (STEM) was developed and used to simulate the acid rain in Korea that occurred on 10 June 1996. The present nested grid system consists of three-grid systems. The coarsest grid system includes China, Korean Peninsula and Japan with the horizontal grid size of 80 km and the finest grid system includes only Korea with the horizontal grid size of 8.9 km. The calculated gas-phase SO 2 and O 3 concentrations agree relatively well with the field measurements. In addition, the model successfully reproduces the measured sulfate and nitrate concentrations in the rain water and futhermore identified the high concentration regions of liquid-phase sulfate and nitrate. In the present simulation conditions, most of the gas-phase of SO 2 and HNO 3 were washed out. A close relationship between wet deposition fluxes and precipitation rates were found for sulfate and nitrate. Finally, the model results also showed that a fine grid size is required to accurately calculate gas-phase concentrations as well as acid deposition fluxes.

A finite difference discretization method for elliptic problems on composite grids

In this paper we discusss a simple finite difference method for the discretization of elliptic boundary value problems on composite grids. For the model problem of the Poisson equation we prove stability of the discrete operator and bounds for the global discretization error. These bounds clearly show how the discretization error depends on the grid size of the coarse grid, on the grid size of the local fine grid and on the order of the interpolation used on the interface. Furthermore, the constants in these bounds do not depend on the quotient of coarse grid size and fine grid size. We also discuss an efficient solution method for the resulting composite grid algebraic problem.

A process‐based model for colluvial soil depth and shallow landsliding using digital elevation data

AbstractA model is proposed for predicting the spatial variation in colluvial soil depth, the results of which are used in a separate model to examine the effects of root strength and vertically varying saturated conductivity on slope stability. The soil depth model solves for the mass balance between soil production from underlying bedrock and the divergence of diffusive soil transport. This model is applied using high‐resolution digital elevation data of a well‐studied site in northern California and the evolving soil depth is solved using a finite difference model under varying initial conditions. The field data support an exponential decline of soil production with increasing soil depth and a diffusivity of about 50 cm2/yr. The predicted pattern of thick and thin colluvium corresponds well with field observations. Soil thickness on ridges rapidly obtain an equilibrium depth, which suggests that detailed field observations relating soil depth to local topographic curvature could further test this model. Bedrock emerges where the curvature causes divergent transport to exceed the soil production rate, hence the spatial pattern of bedrock outcrops places constraints on the production law.The infinite slope stability model uses the predicted soil depth to estimate the effects of root cohesion and vertically varying saturated conductivity. Low cohesion soils overlying low conductivity bedrock are shown to be least stable. The model may be most useful in analyses of slope instability associated with vegetation changes from either land use or climate change, although practical applications may be limited by the need to assign values to several spatially varying parameters. Although both the soil depth and slope stability models offer local mechanistic predictions that can be applied to large areas, representation of the finest scale valleys in the digital terrain model significantly influences local model predictions. This argues for preserving fine‐scale topographic detail and using relatively fine grid sizes even in analyses of large catchments.

The use of Sayre's equation in real space

A method is described for minimizing a least-squares residual to Sayre's equation as a function of electron densities under the constraints that each of the observed structure factors is strictly compatible with the densities, i.e. |Fh| − |Fhobs| = 0. By evaluation of the residual in real space using fine grid sizes, the method enables one to obtain density maps of atomic resolution even with low-resolution data. Numerical calculations have been made at various resolutions for the crystal structure of a small molecule containing only C, N, O and H atoms. It has been found that the residual can be used as a good figure of merit when the resolution of the observed diffraction data is higher than 1.5–1.8 A. With 2.0 A data, however, several unusual structures whose residuals are lower than that of the correct structure have been found. Their existence may indicate a limitation inherent in direct methods based on the principle of `atomicity' in general.

The Determination of Spatial Homogeneity in Multiphase Mixtures

The modifications of the properties of composite materials by controlling the ratio, size, shape, orientation and spatial distribution of the second phase particles is a well known phenomena. Although there are technique available for the quantifying of most of these parameters, there is no established technique for the determination of the spatial homogeneity; yet this property is also highly influental on the behavior of the material. The aim of this paper is to introduce a fully automated technique to determine the spatial homogeneity of second phase particles.The technique presented in this paper was based on the technique reported by Eisenkolb and Lange and Hirlinger. In this technique the image area was divided by a grid having equal size squares (Fig.1). In a homogeneous mixture the proportion of the second phase would be the same in each square. However, because of the finite size and the agglomeration of particles, the proportion of the second phase varies. This variation is best represented by Relative Standard Deviation, Srel, which is defined as the standard deviation divided by the average. As finer grid sizes are used Srel would naturally increase. It was assumed that for a random dispersion Srel increases linearly as the size of the grid squares becomes smaller. In this study it was shown mathematically that this increase becomes faster when agglomerations are present.

Numerical calculations of laminar and turbulent natural convection in water in rectangular channels heated and cooled isothermally on the opposing vertical walls

Natural convection was computed by finite-difference methods using a laminar model for 2 (wide) × 1 and 1 × 1 enclosures for Ra from 10 6 to 10 9 and Pr = 5.12 and 9.17, and a k- ϵ turbulent model for a square enclosure for Ra from 10 10 to 10 11 and Pr = 6.7. The average Nusselt numbers agree well with the correlating equation of Churchill for experimental and computed values. The computed velocity profile along the heated wall is in reasonable agreement with prior experimental values except for the thin boundary layer along the lower part of the wall where a finer grid size than was computationally feasible appears to be necessary. A detailed sensitivity test for constants of the k- ϵ model was also carried out. The velocity profile at the middle height and the average Nusselt number was in even better agreement with the experimental results when the turbulent Prandtl number was increased to four and the constant c 1 was decreased by 10%. A more refined turbulent model and finer grid divisions appear to be desirable, particularly for larger Ra.

Finite-difference methods for calculating steady incompressible flows in three dimensions

A new stable numerical method is described for solving the Navier-Stokes equations for the steady motion of an incompressible fluid in three dimensions. The basic governing equations are expressed in terms of three equations for the velocity components together with three equations for the vorticity components. This gives six simultaneous coupled second-order partial differential equations to be solved. A finite-difference scheme with second-order accuracy is described in which the associated matrices are diagonally dominant. Numerical results are presented for the flow inside a cubical box due to the motion of one of its sides moving parallel to itself for Reynolds numbers up to 100. Several methods of approximation are considered and the effect of different discretizations of the boundary conditions is also investigated. The main method employed is stable for Reynolds numbers greater than 100 but a finer grid size would be required in order to obtain accurate results.

A numerical experiment on the variations of western boundary currents: Part I. Formation of western boundary currents

A numerical experiment is made using a barotropic model for the western boundary currents. The time-dependent, non-linear vorticity equation is integrated with and without the variable of bottom topography. The inertial and frictional boundary flow is resolved with a fine grid size of 10 km. Connection of the western boundary currents with the general circulation is facilitated by giving the fixed Sverdrup transport at the eastern boundary of the model (400 km offshore).