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The paper gives the description of boundary element method (BEM) with subdomains for the solution of convection—diffusion equations with variable coefficients and Burgers’ equations. At first, the whole domain is discretized into K subdomains, in which linearization of equations by representing convective velocity by the sum of constant and variable parts is carried out. Then using fundamental solutions for convection—diffusion linear equations for each subdomain the boundary integral equation (in which the part of the convective term with the constant convective velocity is not included into the pseudo‐body force) is formulated. Only part of the convective term with the variable velocity, which is, as a rule, more than one order less than convective velocity constant part contribution, is left as the pseudo‐source. On the one hand, this does not disturb the numerical BEM—algorithm stability and, on the other hand, this leads to significant improvement in the accuracy of solution. The global matrix, similar to the case of finite element method, has block band structure whereas its width depends only on the numeration order of nodes and subdomains. It is noted, that in comparison with the direct boundary element method the number of global matrix non‐zero elements is not proportional to the square of the number of nodes, but only to the total number of nodal points. This allows us to use the BEM for the solution of problems with very fine space discretization. The proposed BEM with subdomains technique has been used for the numerical solution of one‐dimensional linear steady‐state convective—diffusion problem with variable coefficients and one‐dimensional non‐linear Burgers’ equation for which exact analytical solutions are available. It made it possible to find out the BEM correctness according to both time and space. High precision of the numerical method is noted. The good point of the BEM is the high iteration convergence, which is disturbed neither by high Reynolds numbers nor by the presence of negative velocity zones.

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.

“Velocity of money is a ‘purely statistical concept’ of no causal significance, which varies automatically with changes in the quantity of money in relation to total expenditure,” as concluded in the late 1950s by the well‐known Radcliffe Committee in Great Britain (Kaldor, p. 19). This view, although it has been supported from time to time by prominent economists such as Kaldor and Kahn, is not generally accepted. Velocity and its ‘stability,’ which is closely related to the stability of the demand for money, are considered by many economists to be very important in economic affairs and to constitute an important foundation of the monetarist doctrine.

The gas assisted Iaser heating of engineering surfaces finds wide application in industry. Numerical simulation of the heating process may considerably reduce the cost spent on experimentation. In the present study, 2‐dimensional axisymmetric flow and energy equations are solved numerically using a control volume approach for the case of a gas assisted laser heating of steel surfaces. Various turbulence models including standard k‐ε, k‐ε YAP, low Reynolds number k‐ε and RSTM models are tested. The low Reynolds number k‐ε model is selected to account for the turbulence. Variable properties of both solid and gas are taken into account during the simulation. Air is considered as an assisting gas impinging the workpiece surface coaxially with the laser beam. In order to validate the presently considered methodology, the study is extended to include comparison of present predictions with analytical solution for the case available in the literature. It is found that the assisting gas jet has some influence on the temperature profiles. This effect is minimum at the irradiated spot center and it amplifies considerably in the gas side. In addition, account for the variable properties results in lower surface temperatures as compared to the constant properties case.

The purpose of this paper is to present the design and implementation of a zero‐initial‐velocity self‐motion scheme on a six degrees of freedom (six‐DOF) planar robot manipulator.

In view of the existence of physical limits in an actual robot manipulator, both joint‐angle limits and joint‐velocity limits are initially incorporated into the proposed self‐motion scheme for practical purposes. The proposed self‐motion scheme is then reformulated as a quadratic program (QP) and resolved at the joint‐velocity level. By combining the zero‐initial‐velocity constraint, the resultant QP can prevent the occurrence of a large initial joint velocity. Finally, based on the conversion technique of QP to a linear variational inequality, a numerical computing algorithm is presented to solve the QP and the corresponding self‐motion scheme.

The proposed zero‐initial‐velocity self‐motion scheme eliminates the phenomenon of the abrupt and drastic increase in joint velocity at the beginning of the self‐motion task execution. Simulative and experimental results based on a practical six‐DOF planar robot manipulator further verify the realizability, effectiveness and accuracy of the proposed self‐motion scheme. Based on the simulative results, the joint angle and the joint velocity meet the joint physical constraints.

The paper provides effective methods for handling the physical limits, the design of zero‐initial velocity, and the conversion from joint angle and joint velocity to motor‐driving pulses. Thus, the effective and safe self‐motion control of a manipulator is realized.

The paper describes the design and implementation of a zero‐initial‐velocity self‐motion scheme.

The purpose of this paper is to investigate the effect of exponential viscosity-temperature relation, exponential thermal conductivity-temperature relation and the combined effects of variable viscosity and variable thermal conductivity on steady free convection flow of viscous incompressible fluid in a vertical channel.

The governing equations are solved analytically using regular perturbation method. The analytical solutions are valid for small variations of buoyancy parameter and the solutions are found up to first order for variable viscosity. Since the analytical solutions have a restriction on the values of perturbation parameter and also on the higher order solutions, the authors resort to numerical method which is Runge-Kutta fourth order method.

The skin friction coefficient and the Nusselt number at both the plates are derived, discussed and their numerical values for various values of physical parameters are presented in tables. It is found that an increase in the variable viscosity enhances the flow and heat transfer, whereas an increase in the variable thermal conductivity suppresses the flow and heat transfer for variable viscosity, variable thermal conductivity and their combined effect.

This research is relatively original as, to the best of the authors’ knowledge, not much work is done on the considered problem with variable properties.

The purpose of this paper is to present a solution space searching method to study the initial design of interplanetary low thrust gravity assist trajectory.

For reducing the complexity and nonlinearity of the initial design problem, a sixth degree inverse polynomial shape based approach is brought. Then some improvements are provided for solving the parameters in the shape function and a quasi‐lambert solver is brought through the shape based method, the thrust profile can be generated under the given time of flight, boundary states including positions and velocities for low thrust phase. Combining gravity assist model, the problem is summarized and an improved pruning technique is used for searching the feasible solution space for low thrust gravity assist trajectory.

Using the solution space searching method, the feasible solution region would be generated under the given mission condition. The treatment about gravity assist demonstrates more accurate than previous method. Also another advantage is that the searching method can be used to design different types of mission trajectory, including flyby and rendezvous trajectories.

The method can be used as an efficient approach to search the feasible region for the complex low thrust gravity assist trajectory, and it can provide appropriate initial guesses for the low thrust gravity assist trajectory in mission design phase.

Feasible solution space would be obtained through the searching method. The quasi‐Lambert solver in the paper is found under the shape‐based method and relative improvement, and it shows its availability during the searching process. Through mission trajectory design, the effectiveness of the method is shown.

This paper aims to extend the hybrid atomistic-continuum multiscale method developed by Vu et al. (2016) to study the gas flow problems in long microchannels involving density variations.

The simulation domain is decomposed into three regions: the bulk where the continuous Navier–Stokes and energy equations are solved, the neighbourhood of the wall simulated by molecular dynamics and the overlap region which connects the macroscopic variables (density, velocity and temperature) between the two former regions. For the simulation of long micro/nanochannels, a strategy with multiple molecular blocks all along the fluid/solid interface is adopted to capture accurately the macroscopic velocity and temperature variations.

The validity of the hybrid method is shown by comparisons with a simplified analytical model in the molecular region. Applications to compressible and condensation problems are also presented, and the results are discussed.

The hybrid method proposed in this paper allows cost-effective computer simulations of large-scale problems with an accurate modelling of the transfers at small scales (velocity slip, temperature jump, thin condensation films, etc.).

Describes the solution of implicitly discretized fluid flow equations, for turbulent swirling flows, by means of a new iterative method, based on the PISO algorithm. The technique is based on the splitting of the solution process into a series of steps, where, at each step, pressure operations are dissociated from those on velocities. The split sets of equations are solvable by standard numerical techniques. However, in this work, the influence of turbulent quantities and tangential velocity on the momentum equations is taken into account in the splitting process, through the source terms of the discretized equations. Does this by embedding a predictor and a corrector step for the turbulent quantities and for the tangential velocity into the PISO algorithm. This improvement to the standard PISO algorithm leads to a considerable reduction of the computational effort in achieving the same numerically converged solution. Applies the algorithm, in conjunction with a finite‐volume technique, to simulate two different geometries for two‐dimensional (axisymmetric) isothermal turbulent steady‐flows, with and without swirl. Compares the results with predictions of the same flows obtained other iterative methods (SIMPLE) and (PISO). Shows that the algorithm presented herein always exhibits a better efficiency in getting exactly the same final predictions, as far as the number of iterations for convergence and the required central processing unit time are concerned.

We introduce a second‐order accurate time‐marching pressure‐correction algorithm to accommodate weakly‐compressible highly‐viscous liquid flows at low Mach number. As the incompressible limit is approached (Ma ≈ 0), the consistency of the compressible scheme is highlighted in recovering equivalent incompressible solutions. In the viscous‐dominated regime of low Reynolds number (zone of interest), the algorithm treats the viscous part of the equations in a semi‐implicit form. Two discrete representations are proposed to interpolate density: a piecewise‐constant form with gradient recovery and a linear interpolation form, akin to that on pressure. Numerical performance is considered on a number of classical benchmark problems for highly viscous liquid flows to highlight consistency, accuracy and stability properties. Validation bears out the high quality of performance of both compressible flow implementations, at low to vanishing Mach number. Neither linear nor constant density interpolations schemes degrade the second‐order accuracy of the original incompressible fractional‐staged pressure‐correction scheme. The piecewise‐constant interpolation scheme is advocated as a viable method of choice, with its advantages of order retention, yet efficiency in implementation.