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The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme.

The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method.

Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media.

The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible.

The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers.

The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

This paper seeks to extend the application of the natural neighbour Galerkin method to vibration analysis of fluid‐structure interaction problems.

The natural element method (NEM) which is a meshless technique is used to simulate the vibration analysis of the fluid‐structure interaction systems. The method uses the natural neighbour interpolation for the construction of test and trial functions. Displacement variable is used for both the solid and the fluid domains, whereas the fluid displacement is written as the gradient of a potential function. Two classical examples are considered: free vibration of a flexible cavity filled with liquid and vibration of an open vessel containing liquid. The corresponding eigenvalue problems are solved and the results are compared with the finite element method (FEM) and analytical solutions to show the accuracy and convergence of the method.

The performance of the NEM is investigated in the computation of the vibration modes of the fluid‐structure interaction problems. Good agreement with analytical and FEM solutions are observed. Through the notable obtained results, it is found that the NEM can also be used in vibration analysis of fluid‐structure interaction problems as it has been successfully applied to some problems in solid and fluid mechanics during the recent years.

In spite of notable achievements in solving some problems in solid and fluid mechanics using NEM, the vibration analysis of fluid‐structure interaction problems, as considered in this paper, has not been investigated so far.

The purpose of this paper is to introduce a new methodology to implement periodic and anti‐periodic boundary conditions in the element free Galerkin method (EFGM).

This paper makes use of the interpolating moving least squares (IMLS) in the EFGM to implement periodic and anti‐periodic boundary conditions. This fact allows imposing periodic and anti‐periodic boundary conditions in a way similar to the one used by the finite element method.

EFGM generally uses the moving least squares to obtain its shape functions. So, these functions do not possess the Kronecker delta property. As a consequence, the imposition of essential, as well as periodic and anti‐periodic boundary conditions needs other techniques to do it. When EFGM makes use of IMLS the shape functions satisfy the Kronecker delta property. As consequence the periodic boundary conditions implementation can be done in a direct way, similar to the FEM.

IMLS provides a new way of periodic boundary conditions implementation in EFGM. This kind of implementation provides an easy and direct way in comparison to usual existing methods. With this technique EFGM can now easily take advantage of electrical machines symmetry.

The purpose of this paper is to demonstrate the eligibility of the weighted residual methods (WRMs) applied to Jeffery-Hamel Flow. Selecting the most appropriate method among the WRMs and discussing about Jeffery-Hamel flow's treatment in divergent and convergent channels are the other important purposes of the present research.

Three analytical methods (collocation, Galerkin and least square method) have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the forth order Runge-Kutta numerical method.

The obtained solutions revealed that WRMs can be simple, powerful and efficient techniques for finding analytical solutions in science and engineering non-linear differential equations.

It could be considered as a first endeavor to use the solution of the Jeffery-Hamel flow using these kind of analytical methods along with the numerical approach.

The purpose of this study is an application of the multi-wavelets Galerkin method to delay differential equations with vanishing delay known as Pantograph equation.

The method consists of expanding the required approximate solution at the elements of the Alpert multi-wavelets. Using the operational matrices of integration and wavelet transform matrix, the authors reduce the problem to a set of algebraic equations.

Because of the large size of the system, thresholding is used to obtain a new sparse system, and then this new system is solved to reduce the computational effort and related computer run time. The authors demonstrate that the solutions may be efficiently represented in a multi-wavelets basis because of flexible vanishing moments property of this type of multi-wavelets.

The L₂ convergence of the scheme for the proposed equation has been investigated. A series of numerical tests is provided to demonstrate the validity and applicability of the technique.

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.

Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.

The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.

The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

To study the thermal performance of both co‐current and counter‐current parallel flow heat exchangers. The hot stream is assumed to flow in the middle of two cold streams and exchange heat with them.

The dimensionless governing equations are derived based on the conservation of energy principle and solved using FEM based on subdomain collocation method and Galerkin's method. The results show that the subdomain collocation method is more accurate than the Galerkin's method, as observed when the results obtained are compared with the analytical results for the classical two‐fluid heat exchangers.

The results are presented in terms of effectiveness and number of transfer units (Ntu) for different values of the governing parameters. The governing parameters are the Ntu, the heat capacity ratios, the overall heat transfer coefficient ratio, and the inlet temperatures parameter. The results show that the effectiveness of the three‐fluid heat exchanger is always higher than that of classical two‐fluid flow heat exchanger for fixed values of the governing parameters. The results also show that for fixed values of the governing parameters, the effectiveness of the counter‐current is higher than the co‐current parallel flow three‐fluid heat exchangers.

One‐dimensional governing equations are derived based on the conservation of energy principle. The ranges of the governing parameters are: Ntu (0:5), the heat capacity ratios (0:1,000), the overall heat transfer coefficient ratio (0:2), and the inlet temperatures parameter (0:1).

Both co‐current and counter‐current parallel flow heat exchangers are used in the thermal engineering applications. The design and performance analysis of these heat exchangers are of practical importance.

This paper provides the details of the performance analysis of co‐current and counter‐current parallel flow heat exchangers, which can be used in thermal design.

This paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing.

The authors use a space-time weak formulation of SWEs which exploits continuous Galerkin (cG) in space and discontinuous Galerkin (dG) in time allowing time stepping, also known as cGdG. Such formulations along with SC term have recently been proved to ensure the stability of fully discrete schemes without scarifying the accuracy. However, the resulting scheme is expensive in terms of number of degrees of freedom (DoFs). By using natural adaptivity of wavelet expansions, the authors devise an adaptive algorithm to reduce the number of DoFs.

The proposed algorithm uses DoFs in a dynamic way to capture the shocks in all time steps while keeping the representation of approximate solution sparse. The performance of the proposed scheme is shown through some numerical examples.

An incorporation of wavelets for adaptivity in space-time weak formulations applied for SWEs is proposed.