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The numerical solution of problems involving two‐dimensional flow in an infinite or a semi‐infinite channel is considered. Beyond a certain finite region, where the flow and geometry may be general, a “tail” region is assumed where the flow is potential and the channel is uniform. This situation is typical in many cases of fluid‐structure interaction and flow around obstacles in a channel. The unbounded domain is truncated by means of an artificial boundary B, which separates between the finite computational domain and the “tail.” On B, special boundary conditions are devised. In the finite computational domain, the problem is solved using a finite element scheme. Both non‐local and local artificial boundary conditions are considered on B, and their performance is compared via numerical examples.

Numerical simulation of a fluid flow involves the specification of boundary conditions along all or part of the boundary. Designs a means of handling outflow boundary conditions for the incompressible Navier‐Stokes equations. Addresses through‐flow problems involving the specification of outflow conditions at the synthetic boundary. This outflow boundary condition is applicable to a developing flow problem. The underlying objectives behind designing the boundary condition at the truncated boundary are three‐fold, namely: matching with Navier‐Stokes equations inside the domain; taking both non‐linear and diffusive contributions into account; and ensuring the discrete divergence‐free condition. In order to meet these requirements, follows the concept of a free boundary condition by taking the outflow nodal values of u, v and p as unknowns, which are coupled with the interior unknowns through the surface integrals in the momentum equations. The computed solutions can be legitimately regarded as solutions to conservation equations under consideration when both components of the surface traction vector approach zero. With the convergent property accommodated in the present mixed finite element analysis, the task remains to simply improve the accuracy. Demonstrates the capability of the proposed non‐linear outflow boundary conditions through several benchmark tests.

A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers.

The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF.

The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured.

This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.

Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.

This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).

The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.

To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems, using parallel algorithm.

Parallel solution to the 3‐D incompressible full Navier‐Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time‐step sizes, with Courant‐Friedrichs‐Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non‐overlapping sub‐domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3‐D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied.

It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely.

A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well‐known 3D free‐convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re=2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re=2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.

The purpose of this paper is to propose an efficient/robust numerical algorithm for solving the two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element (FE) technique.

A numerical algorithm was based on the so‐called consistent splitting scheme, which improved the numerical accuracy of the primitive variables. In order to obtain a stable solution, two choices of mixed FEs, the Taylor‐Hood and Crouzeix‐Raviart types, were used. Two mesh layouts were considered; uniform and non‐uniform.

To verify that the proposed scheme had a second‐order accuracy, some numerical results are presented and compared with the known solution. The answer was confirmative. Numerically accurate solutions were obtained for a fixed Prandtl number, Pr=0.71, for a range of the Reynolds number, Re from 100 to 3,000, and for a range of the Richardson number, Ri from 0.001 to 100. The results from these calculations, using the mixed FE consistent splitting scheme, agreed with the existing ones.

Further extensions of this work could include the influence of various choices of Reynolds numbers, Prandtl numbers and Richardson numbers, and the effect of aspect ratio.

The present work was the first to apply a mixed FE in association with the consistent splitting scheme to the mixed convection problem.

The paper describes an approximate method for the direct stress analysis of anisotropic swept cantilever plates, without the usual need for intermediate deflection calculations. The method of analysis employs the Principle of Least Work, in conjunction with the assumption that the load and stress components may be represented with sufficient accuracy by a power series in the chordwise co‐ordinate, the coefficients of this series being functions of the spanwise position only. The validity is thus limited to these loadings for which the series involved are convergent. A system of oblique co‐ordinates is used to simplify the analysis. Particular attention is focused on the parallelogram cantilever plate, subjected to a uniform normal loading and to a system of tip bending moments, twisting moments and shear forces. Theoretical predictions are compared with the results of an experimental investigation.

The aim is to present in this paper an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.

The authors introduce a new orthogonal system of rational functions induced by general Jacobi polynomials with the parameters alpha and beta. It is more flexible in applications. In particular, alpha and beta could be regulated, so that the systems are mutually orthogonal in certain weighted Hilbert spaces.

This approach is applied for solving a non‐linear system two‐point boundary value problem (BVP) on semi‐infinite interval, describing the flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. The new approach reduces the solution of a problem to the solution of a system of algebraic equations.

The paper presents an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.