ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows

We propose a C2-continuous alternating direction implicit (ADI) method for the solution of the streamfunction-vorticity equations governing steady 2D incompressible viscous fluid flows. Discretisation is simply achieved with Cartesian grids. Local two-node integrated radial basis function elements (IRBFEs) [D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong, A C2-continuous control-volume technique based on Cartesian grids and two-node integrated-RBF elements for second-order elliptic problems, CMES: Computer Modeling in Engineering & Sciences 72 (2011) 299-334] are used for the discretisation of the diffusion terms, and then the convection terms are incorporated into system matrices by treating nodal derivatives as unknowns. ADI procedure is applied for the time integration. Following ADI factorisation, the two-dimensional problem becomes a sequence of one-dimensional problems. The solution strategy consists of multiple use of a one-dimensional sparse matrix algorithm that helps saving the computational cost. High levels of accuracy and efficiency of the present methods are demonstrated with solutions of several benchmark problems defined on rectangular and non-rectangular domains

A comprehensive evaluation of polygenic score and genotype imputation performances of human SNP arrays in diverse populations

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Establishing and validating noninvasive prenatal testing procedure for fetal aneuploidies in Vietnam

Noninvasive prenatal testing (NIPT) for fetal aneuploidies has been widely adopted in developed countries. Despite the sharp decrease in the cost of massively parallel sequencing, the technical know-how and skilled personnel are still one of the major limiting factors for applying this technology to NIPT in low-income settings. Here, we present the establishment and validation of our NIPT procedure called triSure for detection of fetal aneuploidies.We established the triSure algorithm based on the difference in proportion of fetal and maternal fragments from the target chromosome to all chromosomes. Our algorithm was validated using a published data set and an in-house data set obtained from high-risk pregnant women in Vietnam who have undergone amniotic testing. Several other aneuploidy calling methods were also applied to the same data set to benchmark triSure performance.The triSure algorithm showed similar accuracy to size-based method when comparing them using published data set. Using our in-house data set from 130 consecutive samples, we showed that triSure correctly identified the most samples (overall sensitivity and specificity of 0.983 and 0.986, respectively) compared to other methods tested including count-based, sized-based, RAPIDR and NIPTeR.We have demonstrated that our triSure NIPT procedure can be applied to pregnant women in low-income settings such as Vietnam, providing low-risk screening option to reduce the need for invasive diagnostic tests

Carbon dioxide reforming of methane over modified iron-cobalt alumina catalyst : Role of promoter

Cobalt-based catalysts are widely employed in methane dry reforming but tend to deactivate quickly due to coke deposits and metal sintering. To enhance the performance, iron, a cost-effective promoter, is added, improving cobalt's metal dispersibility, reducibility, and basicity on the support. This addition accelerates carbon gasification, effectively inhibiting coke deposition. Methods: A series of iron-doped cobalt alumina MFe-5Co/Al2O3 (M= 0, 0.4, 0.8, 1, 2 wt.%) were prepared via simple incipient-wetness impregnation. The catalysts were thoroughly characterized via modern techniques including BET, XRD, H2-TPR, CO2-TPD. Significant findings: The addition of iron had a minimal impact on the properties of γ-Al2O3, but it significantly affected the dispersibility of cobalt. At an optimal dosage of 0.8 wt.%, there was a notable decrease of 29.44% in Co3O4 particle size. However, excessive iron loading induced agglomeration of Co3O4, which was reversible. The presence of iron also resulted in a decrease in the reduction temperature of Co3O4. The material's basicity was primarily influenced by the loading of iron, reaching its highest value of 705.7 μmol CO2 g−1 in the 2Fe-5Co/Al2O3. The correlation between catalytic activity and the physicochemical properties of the material was established. The 0.8Fe-5Co/Al2O3 sample exhibited excellent performance due to the favorable dispersibility of cobalt, its reducibility, and its affordable basicity

High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows

In this paper, 2-node integrated radial basis function elements (IRBFEs)[CMES, vol.72, no.4, pp.299-334, 2011] are further developed for the simulation of incompressible viscous flows in two dimensions. Emphasis is placed on (i) the incorporation of C2-continuous 2-node IRBFEs into the subregion and point collocation frameworks for the discretisation of the stream function-vorticity formulation on Cartesian grids; and (ii) the development of high order upwind schemes based on 2-node IRBFEs for the case of convection-dominant flows. High levels of accuracy and efficiency of the present methods are demonstrated by solutions of several benchmark problems defined on rectangular and non-rectangular domains

RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients

Many important engineering problems have multiple-scale solutions. Thermal conductivity of composite materials, flow in porous media, and turbulent transport in high Reynolds number flows are examples of this type. Direct numerical simulations for these problems typically require extremely large amounts of CPU time and computer memory, which may be too expensive or impossible on the present supercomputers. In this paper, we develop a high order computational method, based on multiscale basis function approach and integrated radial-basis-function (IRBF) approximant, for the solution of multiscale elliptic problems with reduced computational cost. Unlike other methods based on multiscale basis function approach, sets of basis and correction functions here are obtained through $C^2$-continuous IRBF element formulations. High accuracy and efficiency of this method are demonstrated by several one- and two-dimensional examples

An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows

This paper presents a numerical approach for macro-micro multi-scale modelling of visco-elastic fluid flows based on the Integrated Radial Basis Function Networks (IRBFNs) and the Stochastic Simulation Technique (SST). The extra stress is calculated using the Brownian configuration fields (BCFs) technique while the velocity field is locally approximated at a set of collocation points using 1D-IRBFNs. In this approach, the stress is decoupled from the velocity field and computed from the molecular configuration directly without the need for a closed form rheological constitutive equation. The equations governing the macro flow field are discretised using a meshless collocation method where the IRBFN approximants improve the accuracy of the numerical solutions by avoiding the deterioration of accuracy caused by differentiation. As an illustration of the method, the time evolution of the planar Couette flow and the steady state Poiseuille flow are studied for two molecular kinetic models: the Hookean dumbbell and FENE dumbbell models

A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems

This paper presents a new control-volume discretisation method, based on Cartesian grids and integrated-radial-basis-function elements (IRBFEs), for the solution of second-order elliptic problems in one and two dimensions. The governing equation is discretised by means of the control-volume formulation and the division of the problem domain into non-overlapping control volumes is based on a Cartesian grid. Salient features of the present method include (i) an element is defined by two adjacent nodes on a grid line, (ii) the IRBF approximations on each element are constructed using only two RBF centres (a smallest RBF set) associated with the two nodes of the element and (iii) the IRBFE solution is C2-continuous across the interface between two adjacent elements. The first feature guarantees consistency of the flux at control-volume faces. The second feature helps represent curved profiles between 2 adjacent nodes and leads to a sparse and banded system matrix, facilitating the employment of a large number of nodes. The third feature enhances the smoothness of element-based solutions, allowing a better estimation for the physical quantities involving derivatives. Numerical results indicate that (i) the proposed method can work with a wide range of the shapeparameter/RBF-width and (ii) the proposed technique yields more accurate results and faster convergence, especially for the approximation of derivatives, than the standard control-volume technique