Computational and experimental simulation to analyze loss in concrete cover by reinforcement deformation in solid slabs

ABSTRACT Adequate cover thickness contributes to the correct performance of reinforced concrete structures. Spacers are recommended in standards to maintain a concrete cover; however, many regulations do not provide sufficient guidelines for their use, resulting in poor construction. A research program was developed for solid slabs through computational and experimental simulations to minimize errors in the cover by assessing different reinforcement bar diameters and spacer distribution, considering realistic element construction and standards, combining theory with practice. The results show that the use of spacers does not guarantee the design cover for some reinforcement bar diameters, as 4.2 and 5.0 mm, and regardless of the spacer distribution configuration assessed, these meshes undergo permanent deformation, thereby damaging the cover and consequently impact structural performance. Meshes of 6.3 and 8.0 mm diameters present deformation within the cover tolerance. Therefore, it is preferable to choose bigger diameters and larger mesh spacing to guarantee the projected cover, contributing to the correct performance of the structures, solving one of the major problems in this type of construction.

Convergency and Stability of Explicit and Implicit Schemes in the Simulation of the Heat Equation

Some strategies for solving differential equations based on the finite difference method are presented: forward time centered space (FTSC), backward time centered space (BTSC), and the Crank-Nicolson scheme (CN). These are developed and applied to a simple problem involving the one-dimensional (1D) (one spatial and one temporal dimension) heat equation in a thin bar. The numerical implementation in this work can be used as a preamble to introduce a method of solving the heat equation that can be implemented in problems in the area of finances. The results of implementing the software on very fine meshes (unidimensional), and with relatively small-time steps, are shown. Through mesh refinement, it was possible to obtain a better temperature distribution in the thin bar between a range of points. The heat equation was solved numerically by testing both implicit (CN) and explicit (FTSC and BTSC) methods. The examples show that the implemented schemes conform to theoretical predictions and that truncation errors depend on mesh, spacing, and time step.

Detecting Grounding Grid Orientation: Transient Electromagnetic Approach

The configuration is essential to diagnose the status of the grounding grid, but the orientation of the unknown grounding grid is ultimately required to diagnose its configuration explicitly. This paper presents a transient electromagnetic method (TEM) to determine grounding grid orientation without excavation. Unlike the existing pathological solutions, TEM does not enhance the surrounding electromagnetic environment. A secondary magnetic field as a consequence of induced eddy currents is subjected to inversion calculation. The orientation of the grounding grid is diagnosed from the equivalent resistivity distribution against the circle perimeter. High equivalent resistivity at a point on the circle implies the grounding grid conductor and vice versa. Furthermore, various mesh configurations including the presence of a diagonal branch and unequal mesh spacing are taken into account. Simulations are performed using COMSOL Multiphysics and MATLAB to verify the usefulness of the proposed method.

Vertical Resolution Requirements in Atmospheric Simulation

The role of vertical mesh spacing in the convergence of full-physics global atmospheric model solutions is examined for synoptic, mesoscale, and convective-scale horizontal resolutions. Using the MPAS-Atmosphere model, convergence is evaluated for three solution metrics: the horizontal kinetic energy spectrum, the Richardson number probability density function, and resolved flow features. All three metrics exhibit convergence in the free atmosphere for a 15-km horizontal mesh when the vertical grid spacing is less than or equal to 200 m. Nonconvergence is accompanied by noise, spurious structures, reduced levels of mesoscale kinetic energy, and reduced Richardson number peak frequencies. Coarser horizontal mesh solutions converge in a similar manner but contain much less noise than the 15-km solutions for coarse vertical resolution. For convective-scale resolution simulations with 3-km cell spacing on a variable-resolution mesh, solution convergence is almost attained with a vertical mesh spacing of 200 m. The boundary layer scheme is the dominant source of vertical filtering in the free atmosphere. Although the increased vertical mixing at coarser vertical mesh spacing depresses the kinetic energy spectra and Richardson number convergence, it does not produce sufficient dissipation to effectively halt scale collapse. These results confirm and extend the results from a number of previous studies, and further emphasize the sensitivity of the energetics to the vertical mixing formulations in the model.

Experimental and Numerical Investigation of the Growth of an Air/SF6 Turbulent Mixing Zone in a Shock Tube

Shock-induced mixing experiments have been conducted in a vertical shock tube of 130 mm square cross section located at ISAE. A shock wave traveling at Mach 1.2 in air hits a geometrically disturbed interface separating air and SF6, a gas five times heavier than air, filling a chamber of length L up to the end of the shock tube. Both gases are initially separated by a 0.5 μm thick nitrocellulose membrane maintained parallel to the shock front by two wire grids: an upper one with mesh spacing equal to either ms = 1.8 mm or 12.1 mm, and a lower one with a mesh spacing equal to ml = 1 mm. Weak dependence of the mixing zone growth after reshock (interaction of the mixing zone with the shock wave reflected from the top end of the test chamber) with respect to L and ms is observed despite a clear imprint of the mesh spacing ms in the schlieren images. Numerical simulations representative of these configurations are conducted: the simulations successfully replicate the experimentally observed weak dependence on L, but are unable to show the experimentally observed independence with respect to ms while matching the morphological features of the schlieren pictures.

TOWARDS UNDERSTANDING THE INFLUENCE OF GRADIENT RECONSTRUCTION METHODS ON UNSTRUCTURED FLOWSIMULATIONS

In this paper, the formal order of accuracy of three commonly used gradient reconstruction methods is derived. The analysis showed that the Green–Gauss cell based (GGCB) method is intrinsically inconsistent, due to the leading error term that is independent of the mesh spacing. On the other hand, the Green–Gauss node based (GGNB) and the Least Squares cell based (LSCB) methods achieved a minimum of 1st order accuracy regardless of the mesh geometric properties. Implications of the former results were practically tested on four CFD applications to show that in three out of four cases, the LSCB method achieved the highest order of accuracy. In terms of the computational expenses, the GGNB method consumed 9–34% additional time when compared to the fastest converging method in each test case. Both the GGCB and the LSCB methods consumed nearly the same computational time to reach convergence.

Locally-orthogonal unstructured grid-generation for general circulation modelling on the sphere*

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate high-quality staggered Voronoi/Delaunay dual meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Delaunay-refinement technique allows for the generation of unstructured grids that satisfy a priori constraints on minimum mesh-quality. The initial staggered Voronoi/Delaunay tessellation is iteratively improved through hill-climbing optimisation techniques. Such an approach is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling. The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.

Numerical Analysis of the Immersed Boundary Method for Cell-Based Simulation

Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behaviour, models that consider cells as individual objects are becoming a common tool to study how processes at the single-cell level affect collective dynamics and determine tissue size, shape and function. However, there often remains no comprehensive account of these models, their method of solution, computational implementation or analysis of parameter scaling, hindering our ability to utilise and accurately compare different models. Here we present an effcient, open-source implementation of the immersed boundary method (IBM), tailored to simulate the dynamics of cell populations. This approach considers the dynamics of elastic membranes, representing cell boundaries, immersed in a viscous Newtonian fluid. The IBM enables complex and emergent cell shape dynamics, spatially heterogeneous cell properties and precise control of growth mechanisms. We solve the model numerically using an established algorithm, based on the fast Fourier transform, providing full details of all technical aspects of our implementation. The implementation is undertaken within Chaste, an open-source C++ library that allows one to easily change constitutive assumptions. Our implementation scales linearly with time step, and subquadratically with mesh spacing and immersed boundary node spacing. We identify the relationship between the immersed boundary node spacing and fluid mesh spacing required to ensure fluid volume conservation within immersed boundaries, and the scaling of cell membrane stiffness and cell-cell interaction strength required when refining the immersed boundary discretization. This study provides a recipe allowing consistent parametrisation of IBM models.

Mesh Spacing Estimates and Efficiency Considerations for Moving Mesh Systems

Adaptive numerical methods for solving partial differential equations (PDEs) that control the movement of grid points are called moving mesh methods. In this paper, these methods are examined in the case where a separate PDE, that depends on a monitor function, controls the behavior of the mesh. This results in a system of PDEs: one controlling the mesh and another solving the physical problem that is of interest. For a class of monitor functions resembling the arc length monitor, a trade off between computational efficiency in solving the moving mesh system and the accuracy level of the solution to the physical PDE is demonstrated. This accuracy is measured in the density of mesh points in the desired portion of the domain where the function has steep gradient. The balance of computational efficiency versus accuracy is illustrated numerically with both the arc length monitor and a monitor that minimizes certain interpolation errors. Physical solutions with steep gradients in small portions of their domain are considered for both the analysis and the computations.