Anisotropic adaptivity for the finite element solutions of three-dimensional convection-dominated problems

Convection-dominated problems are typified by the presence of strongly directional features such as shock waves or boundary layers. Resolution of numerical solutions using an isotropic mesh can lead to unnecessary refinement in directions parallel to such features. This is particularly important in three dimensions where the grid size increases rapidly during conventional isotropic refinement procedures. In this work, we investigate the use of adaptive finite element methods using anisotropic mesh refinement strategies for convection-dominated problems. The strategies considered here aim to resolve directional features without excessive resolution in other directions, and hence achieve accurate solutions more efficiently. Two such strategies are described here: the first based on minimization of the least-squares residual; the second based on minimizing a finite element error estimate. These are incorporated into an hr-adaptive finite element method and tested on a simple model problem

A multilevel approach for obtaining locally optimal finite element meshes

In this paper we consider the adaptive finite element solution of a general class of variational problems using a combination of node insertion, node movement and edge swapping. The adaptive strategy that is proposed is based upon the construction of a hierarchy of locally optimal meshes starting with a coarse grid for which the location and connectivity of the nodes is optimized. This grid is then locally refined and the new mesh is optimized in the same manner. Results presented indicate that this approach is able to produce better meshes than those possible by more conventional adaptive strategies and in a relatively efficient manner

Mathematical Modelling of Chemical Diffusion through Skin using Grid-based PSEs

A Problem Solving Environment (PSE) with connections to remote distributed Grid processes is developed. The Grid simulation is itself a parallel process and allows steering of individual or multiple runs of the core computation of chemical diffusion through the stratum corneum, the outer layer of the skin. The effectiveness of this Grid-based approach in improving the quality of the simulation is assessed

Influence of activator type on reaction kinetics, setting time, and compressive strength of alkali-activated mineral wools

Alkali activation is a promising utilisation route for mineral wool wastes, due to suitable chemical composition, high reactivity, and surface area. One key factor in the development of alkali-activated binders is the selection of the suitable alkali activator. Here, the effect of sodium hydroxide, sodium silicate, sodium aluminate, and sodium carbonate solution on the alkali-activation kinetics of two main types of mineral wools, stone wool and glass wool, is investigated. Setting time and compressive strength development results are presented, which are explained and discussed in the context of isothermal calorimeter data obtained at temperature of 40 °C. Sodium hydroxide and sodium silicate solutions provided fast reaction with both mineral wools, evidenced by high heat release, high early strength, and fast setting. The reaction with sodium aluminate solution took several days to initiate, but it produced high compressive strength after 28 days of curing with both mineral wools. Glass wool reacted and hardened rapidly with sodium carbonate solution, but stone wool reacted slowly with sodium carbonate and exhibited a low extent of reaction, likely due to lower extent of reaction of stone wool under less alkaline conditions. These results show that mineral wool alkali activation kinetics and binder gel formation are controlled by the activator type and highlight the importance of choosing the most appropriate activator for each desired application

Nanostructural evolution of alkali-activated mineral wools

Mineral wools are the most widely used building insulation material worldwide. Annually, 2.5 million tonnes of mineral wool waste are generated in the EU alone, and this is a largely unutilised material that is landfilled or incinerated. However, mineral wool wastes are promising precursors for production of alkali-activated cementitious binders due to their favourable chemical and mineralogical composition and high surface area. Alkali-activation is therefore a valuable route for valorisation of large quantities of mineral wool waste. This study resolves the phase assemblage and nanostructure of reaction products formed upon alkali activation of stone wool and glass wool by sodium hydroxide and sodium silicate solutions with X-ray diffraction, electron microscopy and solid state nuclear magnetic resonance spectroscopy experiments probing ^27Al and ^29Si. The stone wool-based alkali-activated binder comprises an amorphous sodium- and aluminium-substituted calcium silicate hydrate (C-(N-)A-S-H) gel, an amorphous sodium aluminosilicate hydrate (N-A-S-H) gel and small amounts of the layered double hydroxide phase quintinite and zeolite F. The glass wool-based alkali-activated binder comprises an amorphous Ca- and Al-substituted sodium silicate (N-(C-)(A-)S–H) gel. Gel chemical composition and reaction kinetics of alkali-activated mineral wools are shown to be dependent on the activating solution chemistry, with reaction rate and extent promoted by inclusion of a source of soluble Si in the reaction mixture. This work provides the most advanced description of the chemistry and structure of alkali-activated mineral wools to date, yielding new insight that is essential in developing valorisation pathways for mineral wools by alkali activation and providing significant impetus for development of sustainable construction materials

Mesh shape and anisotropic elements : theory and practice

The relationship between the shape of finite elements in unstructured meshes and the error that results in the numerical solution is of increasing importance as finite elements are used to solve problems with highly anisotropic and, often, very complex solutions. This issue is explored in terms of a priori and a posteriori error estimates, and through consideration of the practical issues associated with assessing element shape quality and implementing an adaptive finite element solver

A Three-Dimensional, One-Field, Fictitious Domain Method for Fluid-Structure Interactions

In this article we consider the three-dimensional numerical simulation of Fluid-Structure Interaction (FSI) problems involving large solid deformations. The one-field Fictitious Domain Method (FDM) is introduced in the framework of an operator splitting scheme. Three-dimensional numerical examples are presented in order to validate the proposed approach: demonstrating energy stability and mesh convergence; and extending two dimensional benchmarks from the FSI literature. New three dimensional benchmarks are also proposed

Phase evolution of Na2O–Al2O3–SiO2–H2O gels in synthetic aluminosilicate binders

This study demonstrates the production of stoichiometrically controlled alkali-aluminosilicate gels (‘geopolymers’) via alkali-activation of high-purity synthetic amorphous aluminosilicate powders. This method provides for the first time a process by which the chemistry of aluminosilicate-based cementitious materials may be accurately simulated by pure synthetic systems, allowing elucidation of physicochemical phenomena controlling alkali-aluminosilicate gel formation which has until now been impeded by the inability to isolate and control key variables. Phase evolution and nanostructural development of these materials are examined using advanced characterisation techniques, including solid state MAS NMR spectroscopy probing 29Si, 27Al and 23Na nuclei. Gel stoichiometry and the reaction kinetics which control phase evolution are shown to be strongly dependent on the chemical composition of the reaction mix, while the main reaction product is a Na2O–Al2O3–SiO2–H2O type gel comprised of aluminium and silicon tetrahedra linked via oxygen bridges, with sodium taking on a charge balancing function. The alkali-aluminosilicate gels produced in this study constitute a chemically simplified model system which provides a novel research tool for the study of phase evolution and microstructural development in these systems. Novel insight of physicochemical phenomena governing geopolymer gel formation suggests that intricate control over time-dependent geopolymer physical properties can be attained through a careful precursor mix design. Chemical composition of the main N–A–S–H type gel reaction product as well as the reaction kinetics governing its formation are closely related to the Si/Al ratio of the precursor, with increased Al content leading to an increased rate of reaction and a decreased Si/Al ratio in the N–A–S–H type gel. This has significant implications for geopolymer mix design for industrial applications

Activation of PTHrP-cAMP-CREB1 signaling following p53 loss is essential for osteosarcoma initiation and maintenance

Mutations in the P53 pathway are a hallmark of human cancer. The identification of pathways upon which p53-deficient cells depend could reveal therapeutic targets that may spare normal cells with intact p53. In contrast to P53 point mutations in other cancer, complete loss of P53 is a frequent event in osteosarcoma (OS), the most common cancer of bone. The consequences of p53 loss for osteoblastic cells and OS development are poorly understood. Here we use murine OS models to demonstrate that elevated Pthlh (Pthrp), cAMP levels and signalling via CREB1 are characteristic of both p53-deficient osteoblasts and OS. Normal osteoblasts survive depletion of both PTHrP and CREB1. In contrast, p53-deficient osteoblasts and OS depend upon continuous activation of this pathway and undergo proliferation arrest and apoptosis in the absence of PTHrP or CREB1. Our results identify the PTHrP-cAMP-CREB1 axis as an attractive pathway for therapeutic inhibition in OS.Mannu K Walia, Patricia MW Ho, Scott Taylor, Alvin JM Ng, Ankita Gupte, Alistair M Chalk, Andrew CW Zannettino, T John Martin, Carl R Walkle