A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems

This paper presents a second-order continuity non-overlapping domain decomposition (DD) technique for numerically solving second-order elliptic problems in two-dimensional space. The proposed DD technique uses integrated Chebyshev polynomials to represent the solution in subdomains. The constants of integration are utilized to impose continuity of the second-order normal derivative of the solution at the interior points of subdomain interfaces. To also achieve a C2 (C squared) function at the intersection of interfaces, two additional unknowns are introduced at each intersection point. Numerical results show that the present DD method yields a higher level of accuracy than conventional DD techniques based on differentiated Chebyshev polynomials

A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity flow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids

A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains

In this paper, an integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for biharmonic boundary-value problems, J. Comput. Appl. Math. 201 (1) (2007) 30–47] is further developed for the case of irregularly shaped domains. The problem domain is embedded in a domain of regular shape, which facilitates the use of tensor product grids. Two relevant important issues, namely the description of the boundary of the domain on a tensor product grid and the imposition of double boundary conditions, are handled effectively by means of integration constants. Several schemes of the integral collocation formulation are proposed, and their performances are numerically investigated through the interpolation of a function and the solution of 1D and 2D biharmonic problems. Results obtained show that they yield spectral accuracy

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures

This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement

Computation of transient viscous flows using indirect radial basis function networks

In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are achieved using relatively low numbers of data points

An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings

A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows

A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids

ASSESSING THE ADAPTIVE CAPACITY OF HOUSEHOLDS TO CLIMATE CHANGE: A CASE STUDY IN QUANG DIEN DISTRICT, THUA THIEN HUE PROVINCE

Abstract: This study aims to identify the adaptation capacity undertaken by households in response to natural disasters and climate changes (CC). A total of 100 households in two communes including Quang Phuoc and Quang Cong, Quang Dien district were interviewed. The findings indicate that in the last few years, these communes have been badly affected by various types of natural hazards, including typhoons, floods, droughts and, and extremely cold weather. The study demonstrates that the adaptive capacity index in Quang Cong is significantly lower than that in Quang Phuoc (0.50 and 0.52). Also, the current adaptation actions of local households in response to natural disasters and CC have focused on short-term actions only. On the basis of the findings, the study proposes key recommendations to local households in Quang Dien district to effectively mitigate and adapt to natural disasters and CC. The recommendations encompass three groups, namely (i) raising awareness and understanding about CC; (ii) improving the infrastructure system; and (iii) diversifying livelihood strategies to increase income.Keywords: climate change, natural disasters, adaptive capacity, inde

Imposition of physical parameters in dissipative particle dynamics

In the mesoscale simulations by the dissipative particle dynamics (DPD), the motion of a fluid is modelled by a set of particles interacting in a pairwise manner, and it has been shown to be governed by the Navier–Stokes equation, with its physical properties, such as viscosity, Schmidt number, isothermal compressibility, relaxation and inertia time scales, in fact its whole rheology resulted from the choice of the DPD model parameters. In this work, we will explore the response of a DPD fluid with respect to its parameter space, where the model input parameters can be chosen in advance so that (i) the ratio between the relaxation and inertia time scales is fixed; (ii) the isothermal compressibility of water at room temperature is enforced; and (iii) the viscosity and Schmidt number can be specified as inputs. These impositions are possible with some extra degrees of freedom in the weighting functions for the conservative and dissipative forces. Numerical experiments show an improvement in the solution quality over conventional DPD parameters/weighting functions, particularly for the number density distribution and computed stresses

BEM-RBF approach for viscoelastic flow analysis

A new BE-only method is achieved for the numerical solution of viscoelastic flows. A decoupled algorithm is chosen where the fluid is considered as being composed of an artificial Newtonian component and the remaining component is accordingly defined from the original constitutive equation. As a result the problem is viewed as that of solving for the flow of a Newtonian liquid with the non-linear viscoelastic effects acting as a pseudo body force. Thus the general solution is obtained by adding a particular solution to the homogeneous one. The former is obtained by a BEM for the base Newtonian fluid and the latter is obtained analytically by approximating the pseudo body force in terms of suitable radial basis functions (RBFs). Embedded in the approximation of the pseudo body force is the calculation of the polymer stress. This is achieved by solving the constitutive equation using RBF networks (RBFNs). Both the calculations of the particular solution and the polymer stress are therefore meshless and the resultant BEM-RBF method is a BE-only method. The complete elimination of any structured domain discretisation is demonstrated with a number of flow problems involving the Upper Convected Maxwell (UCM) and the Oldroyd-B fluids