From ‘Orthogonal’ Sprawl to ‘Curvilinear’ Dense: Assessing Accessibility Indices for Urban Networks of Social Housing in UAE

The shift towards designing more dense urban social housing neighbourhoods has started with the embracing of urban sustainability principles by the UAE government since the beginning of the 21st century. The assessment of the recent neighbourhoods designs still lacks concrete evidence about their expected performance especially for pedestrian mobility networks. This concern is gaining further significance with the noticeable tendency of most of the recent urban designs towards developing organic and curvilinear networks instead of the conventional orthogonal grids of the mobility networks that distinguished the traditionally designed neighbourhoods in the country. To bridge this gap, the research comparatively and quantitively analysed the accessibility performance indicators of both of the traditional and the modern urban network designs. The research adopted the Case Study method with quantitative investigation tools that are fundamental to Urban Network Analysis, especially in relation to Accessibility. The simulation of the urban networks of two selected urban social housing neighbourhood forms, representing the networks of both the traditional urban orthogonal sprawl and the recent curvilinear dense one, were utilized employing the UNA toolbox. Three complementary Accessibility Indices were analysed including: Reach, Gravity and Straightness. Through this analysis, the aspects that affected the accessibility performance of the two urban form paradigms and the problems that have been associated with the designs of the urban networks of the new social housing projects, have been revealed. It became evident that the denser urban form was not sufficient in enabling more accessible facilities in the recent neighbourhoods designs. The orthogonal grid, even with its very low Floor Area Ratio showed better performance of in the three accessibility indices especially the Straightness index, if compared with the much denser curvilinear grid with it ‘naturally longer’ pattern. The inefficient number and the inappropriate distribution locally provided facilities in relation to the pedestrian mobility networks have contributed to these disappointing results. So, it is essential to include this and/or similar urban network quantitative simulation tools to help develop genuinely sustainable urban forms for this significant type of urban development in the UAE cities.

A High-Order Finite-Difference Method on Staggered Curvilinear Grids for Seismic Wave Propagation Applications with Topography

ABSTRACT We developed a 3D elastic wave propagation solver that supports topography using staggered curvilinear grids. Our method achieves comparable accuracy to the classical fourth-order staggered grid velocity–stress finite-difference method on a Cartesian grid. We show that the method is provably stable using summation-by-parts operators and weakly imposed boundary conditions via penalty terms. The maximum stable timestep obeys a relationship that depends on the topography-induced grid stretching along the vertical axis. The solutions from the approach are in excellent agreement with verified results for a Gaussian-shaped hill and for a complex topographic model. Compared with a Cartesian grid, the curvilinear grid adds negligible memory requirements, but requires longer simulation times due to smaller timesteps for complex topography. The code shows 94% weak scaling efficiency up to 1014 graphic processing units.

3D Seismic-Wave Modeling with a Topographic Fluid–Solid Interface at the Sea Bottom by the Curvilinear-Grid Finite-Difference Method

ABSTRACT The curvilinear-grid finite-difference method (FDM), which uses curvilinear coordinates to discretize the nonplanar interface geometry, is extended to simulate acoustic and seismic-wave propagation across the fluid–solid interface at the sea bottom. The coupled acoustic velocity-pressure and elastic velocity-stress formulation that governs wave propagation in seawater and solid earth is expressed in curvilinear coordinates. The formulation is solved on a collocated grid by alternative applications of forward and backward MacCormack finite difference within a fourth-order Runge–Kutta temporal integral scheme. The shape of a fluid–solid interface is discretized by a curvilinear grid to enable a good fit with the topographic interface. This good fit can obtain a higher numerical accuracy than the staircase approximation in the conventional FDM. The challenge is to correctly implement the fluid–solid interface condition, which involves the continuity of tractions and the normal component of the particle velocity, and the discontinuity (slipping) of the tangent component of the particle velocity. The fluid–solid interface condition is derived for curvilinear coordinates and explicitly implemented by a domain-decomposition technique, which splits a grid point on the fluid–solid interface into one grid point for the fluid wavefield and another one for the solid wavefield. Although the conventional FDM that uses effective media parameters near the fluid–solid interface to implicitly approach the boundary condition conflicts with the fluid–solid interface condition. We verify the curvilinear-grid FDM by conducting numerical simulations on several different models and compare the proposed numerical solutions with independent solutions that are calculated by the Luco-Apsel-Chen generalized reflection/transmission method and spectral-element method. Besides, the effects of a nonplanar fluid–solid interface and fluid layer on wavefield propagation are also investigated in a realistic seafloor bottom model. The proposed algorithm is a promising tool for wavefield propagation in heterogeneous media with a nonplanar fluid–solid interface.

An Overset Grid Finite-Difference Algorithm to Simulating Elastic Wave Propagation in Media with Complex Free Surface Topography

We present an overset grid algorithm to simplify the difficulty of curvilinear grid generation and increase the computational efficiency for seismic wavefield modeling by employing the finite-difference method in areas with complex surface topography. The overset grid comprises a Cartesian grid block and an approximately orthogonal curvilinear grid block. The Cartesian grid covers most of the simulation domain, while the curvilinear grid discretizes the near-surface topography. The Cartesian grid and curvilinear grid overlap each other arbitrarily. We use sixth-order explicit Lagrangian interpolation to exchange data between the Cartesian and curvilinear grids, which is shown to be sufficiently accurate. We also find that spatially smoothing the source term is important for reducing strong artificial reflections when the source is near the overlapping zone. Finally, numerical tests are performed to verify that the proposed overset grid is well suited for the effective numerical simulation of seismic wave propagation.

Application of the Regional Ocean Modelling System (ROMS) for Baltic Sea area

<p>The Regional Ocean Modelling System has been begun to implement for region of Baltic Sea.  A preliminary curvilinear grid with horizontal resolution ca. 2.3 km has been prepared based on the grid, which was used in previous application in our research group (in Parallel Ocean Program and in standalone version of Los Alamos Sea Ice Model - CICE).  Currently the grid has 30 sigma layers, but the final number of levels will be adjusted accordingly.</p><p>So far we’ve successfully compiled the model on our machine, run test cases and created Baltic Sea case, which is working with mentioned Baltic grid. The following parameters: air pressure, humidity, surface temperature, long and shortwave radiation, precipitation and wind components are used as an atmospheric forcing. The data arrive from our operational atmospheric model - Weather Research and Forecasting Model (WRF).</p><p>Our main goal is to create efficient system for hindcast and forecast simulations of Baltic Sea together with sea ice component by coupling ROMS with CICE. The reason for choosing these two models is an active community that takes care about model’s developments and updates. Authors also intend to work more closely with the CICE model to improve its agreement with satellite measurements in the Baltic region.<br><br>Calculations were carried out at the Academic Computer Centre in Gdańsk.</p>

IZOGRID - A new tool for setting up orthogonal curvilinear grids for oceanic modeling

<p>Virtually all modern structured-grid ocean modeling codes are written in orthogonal curvilinear coordinates in horizontal directions, yet the overwhelming majority of modeling studies are done using very simple grid setups - mostly rectangular patches of Mercator grids rotated to proper orientation.  Furthermore, in communities like ROMS, we even observe decline in both interest and skill of creating curvilinear grids over long term.  This is caused primarily by the dissatisfaction with the existing tools and procedures for grid generation due to inability to achieve acceptable level of orthogonality errors.  Clearly, this causes underutilization of full potential of the modeling codes.</p><p>To address these issues, a new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a compile-once - use forever software package.  Theoretically one can use Schwartz-Christoffel conformal transform to project a curvilinear contour onto rectangle, then draw a Cartesian grid on it, and, finally, apply the inverse transform (the one which maps the rectangle back to the original contour) to the Cartesian grid in order to obtain the orthogonal curvilinear grid which fits the contour.  However, in the general case, the forward transform is an iterative algorithm of Ives and Zacharias (1989), and it is not easily invertible, nor it is feasible to apply it to a two-dimensional object (grid) as opposite to just one-dimensional (contour) because of very large number of operations.  To circumvent this, the core of the new algorithm is essentially based on the numerical solution of the inverse problem by an iterative procedure - finding such distribution of grid points along the sides of curvilinear contour, that the direct conformal mapping of it onto rectangle turns this distribution into uniform one along each side of the rectangle.  Along its way, this procedure also finds the correct aspect ratio, which makes it possible to automatically chose the numbers of grid points in each direction to yield locally the same grid spacing in both horizontal directions.  The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure.  Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving a Dirichlet elliptic problem.  The latter is fairly standard, except that we use "mehrstellenverfahren" discretization, which yields fourth-order accuracy in the case of equal grid spacing in both directions.  The curvilinear contour is generated using splines (cubic or quintic) passing through the user-specified reference points, and, unlike all previous tools designed for the same purpose, it guarantees by the construction to yield the exact 90-degree angles at the corners of the curvilinear perimeter of grid.</p><p>Overall, with the combination of all the new features, it is shown that it is possible to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes in both directions are equal to each other.</p>

DYAMOND-II simulations with IFS-FESOM2

<p>This presentation will give an overview about an ongoing collaboration between the European Centre for Medium-Range Weather Forecasts (ECMWF) and the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI). Our recent development is a single-executable coupled configuration of the Integrated Forecasting System (IFS) and the Finite Volume Sea Ice-Ocean Model, FESOM2. This configuration is set up to participate in the DYAMOND project alongside ECMWF’s default IFS-NEMO configuration. IFS-FESOM2 and IFS-NEMO are tentative models to generate “Digital Twin” storm-scale, coupled simulations as envisioned in the European Destination Earth (DestinE) and Next Generation Earth Modelling Systems (NextGEMS) projects.</p><p>FESOM2 has a novel dynamical core that supports multi-resolution triangular grids. The model and its predecessor FESOM1 have been used in many studies over the last decade, with a focus on the role of the polar regions in global ocean circulation. The impact of eddy-permitting and locally eddy-resolving resolution has been addressed in CMIP6 and HighResMIP simulations as part of the AWI-CM-1-1 global climate model, while simulations with up to 1km resolution in the Arctic Ocean have been performed in stand-alone mode.</p><p>Initially, two coupled IFS-FESOM2 configurations have been tested: A coarse-resolution setup with a nominal 1° ocean, and a DYAMOND-II configuration with 0.25° ocean and IFS at 4.5km global resolution on average. For the latter configuration, FESOM2 is mimicking the “ORCA025” tri-polar curvilinear grid of the NEMO model, whose grid boxes have been split into triangles. Initialisation is from ECMWF’s analysis for IFS and NEMO, and from an ERA5-forced ocean spin-up for FESOM2. We discuss technical challenges with respect to the hybrid OpenMP and MPI parallelization in a single-executable context, describe a novel strategy for resource-efficient writing of model output, and summarise future applications such as exploring the impact of flexible FESOM2 grid configurations on the atmosphere - with ocean simulations that resolve leads in sea ice and ocean eddies almost everywhere.</p>

The mapping of raster images on plane isometric grid

Drawing images on curvilinear shapes with the least distortion takes place in many design tasks. In most ways, build a grid, each elementary cell of which is painted a given color. In this problem it is necessary to solve two main problems: the first - to carry out the formation of a given curvilinear grid with elementary cells in the form of squares, which are called isometric (or isothermal); the second is to paint each cell of the curved area with the corresponding pixel color of the original raster The aim of the study is to reveal the way of displaying raster images on flat curvilinear areas represented by isometric grids, and with the help of a computer model in the Maple symbolic algebra to analyze the influence of isometric grid parameters on the position and size of displayed raster images. The mapping of images onto curvilinear forms with minimal distortion takes place in many design tasks. A method of conformal mapping of arbitrary raster images onto plane curvilinear region is proposed, which are represented by isometric (also called isothermal) grids. The essence of the proposed method is as follows. Any raster image, for example, digital photography in jpg format, is characterized by the dimensions N×M - the number of pixels in width and height. In addition, each pixel has a color and brightness, which are arranged in rows and columns. To apply a raster image to a curvilinear region, it is also necessary to divide the curvilinear domain into N×M, the number of elementary squares, each of which is assigned the corresponding color from the raster. The influence and arguments of the various isometric grids constructed on the sizes and positions of an arbitrary raster image are investigated in the article. It is shown how the isometric grid, depending on and localizes the raster image - it can be located both within the limits of the isometric grid coordinate lines and beyond it, can also be oriented in different directions with respect to the and coordinate lines. It is shown the possibility of scaling a raster image that can be performed relative to the relative dimensions of an isometric grid. Since there is a correspondence between the pixel matrix of the original raster image and the - cells of the isometric grid, the rotation of the image will affect its position in the isometric grid. For example, rotating the original bitmap image at an angle 90 degrees will change its location on a plane isometric grids – from along the coordinate lines to along the coordinate lines. Note that, the curvilinear cells of the constructed isometric grids differ somewhat from the shape of the squares because the values and of the corresponding arguments and of their coordinate lines were taken somewhat too large. Otherwise, cells would degenerate into points and the corresponding grid image would not be so clear.

Interaction of a Solitary Wave with Vertical Fully/Partially Submerged Circular Cylinders with/without a Hollow Zone

In this article, a three-dimensional, fully nonlinear potential wave model is applied based on a curvilinear grid system. This model calculates the wave action on a fully/partially submerged vertical cylinder with or without a hollow zone. As basic verification, a solitary wave hitting a single fully or partially submerged circular cylinder is tested, and our numerical results agree with the experimental results obtained by others. The influence of cylinder immersion depth and size on the wave elevation change on the cylinder surface is considered. The model is also applied to investigate the wave energy of a solitary wave passing through a hollow circular cylinder to determine the effect of the size and draft on the wave oscillating in the hollow zone.

A Rapid Forecasting and Mapping System of Storm Surge and Coastal Flooding

A prototype of an efficient and accurate rapid forecasting and mapping system (RFMS) of storm surge is presented. Given a storm advisory from the National Hurricane Center, the RFMS can generate a coastal inundation map on a high-resolution grid in 1 min (reference system Intel Core i7–3770K). The foundation of the RFMS is a storm surge database consisting of high-resolution simulations of 490 optimal storms generated by a robust storm surge modeling system, Curvilinear-Grid Hydrodynamics in 3D (CH3D-SSMS). The RFMS uses an efficient quick kriging interpolation scheme to interpolate the surge response from the storm surge database, which considers tens of thousands of combinations of five landfall parameters of storms: central pressure deficit, radius to maximum wind, forward speed, heading direction, and landfall location. The RFMS is applied to southwest Florida using data from Hurricane Charley in 2004 and Hurricane Irma in 2017, and to the Florida Panhandle using data from Hurricane Michael in 2018 and validated with observed high water mark data. The RFMS results agree well with observation and direct simulation of the high-resolution CH3D-SSMS. The RFMS can be used for real-time forecasting during a hurricane or “what-if” scenarios for mitigation planning and preparedness training, or to produce a probabilistic flood map. The RFMS can provide more accurate surge prediction with uncertainties if NHC can provide more accurate storm forecasts in the future. By incorporating storms for future climate and sea level rise, the RFMS could be used to generate future flood maps for coastal resilience and adaptation planning.