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The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction.

The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence.

The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency.

Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients.

The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well.

Several test problems are provided to confirm the validity and efficiently of the proposed method.

For the first time, some famous examples are solved by using the proposed high-order technique.

The purpose of this paper is to present an immersed volume method that accounts for solid conductive bodies (hat‐shaped disk) in calculation of time‐dependent, three‐dimensional, conjugate heat transfer and fluid flow.

The incompressible Navier‐Stokes equations and the heat transfer equations are discretized using a stabilized finite element method. The interface of the immersed disk is defined and rendered by the zero isovalues of a level set function. This signed distance function allows turning different thermal properties of each component into homogeneous parameters and it is coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. A monolithic approach is used to solve a single set of equations for both fluid and solid with different thermal properties.

In the proposed immersion technique, only a single grid for both air and solid is considered, thus, only one equation with different thermal properties is solved. The sharp discontinuity of the material properties was captured by an anisotropic refined solid‐fluid interface. The robustness of the method to compute the flow and heat transfer with large materials properties differences is demonstrated using stabilized finite element formulations. Results are assessed by comparing the predictions with the experimental data.

The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfer flow of natural convection, conduction and radiation in a cubic enclosure with the presence of a conduction body. A previous knowledge of the heat transfer coefficients between the disk and the fluid is no longer required. The heat exchange at the interface is solved and dealt with naturally.

The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH).

The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically.

It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH.

This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids.

Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production.

Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration.

The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

Two-dimensional (2D) problems are governed by unsteady anisotropic modified-Helmholtz equation of time–space dependent coefficients are considered. The problems are transformed into a boundary-only integral equation which can be solved numerically using a standard boundary element method (BEM). Some examples are solved to show the validity of the analysis and examine the accuracy of the numerical method.

The 2D problems which are governed by unsteady anisotropic modified-Helmholtz equation of time–space dependent coefficients are solved using a combined BEM and Laplace transform. The time–space dependent coefficient equation is reduced to a time-dependent coefficient equation using an analytical transformation. Then, the time-dependent coefficient equation is Laplace transformed to get a constant coefficient equation, which can be written as a boundary-only integral equation. By utilizing a BEM, this integral equation is solved to find numerical solutions to the problems in the frame of the Laplace transform. These solutions are then inversely transformed numerically to obtain solutions in the original time–space frame.

The main finding of this research is the derivation of a boundary-only integral equation for the solutions of initial-boundary value problems governed by a modified-Helmholtz equation of time–space dependent coefficients for anisotropic functionally graded materials with time-dependent properties.

The originality of the research lies on the time dependency of properties of the functionally graded material under consideration.

In the process of building the “Belt and Road” and “Bright Road” community of interests between China and Kazakhstan, this paper proposes the construction of an inland nuclear power plant in Kazakhstan. Considering the uncertainty of investment in nuclear power generation, the authors propose the MGT (Monte-Carlo and Gaussian Radial Basis with Tensor factorization) utility evaluation model to evaluate the risk of investment in nuclear power in Kazakhstan and provide a relevant reference for decision making on inland nuclear investment in Kazakhstan.

Based on real options portfolio combined with a weighted utility function, this study takes into account the uncertainties associated with nuclear power investments through a minimum variance Monte Carlo approach, proposes a noise-enhancing process combined with geometric Brownian motion in solving complex conditions, and incorporates a measure of investment flexibility and strategic value in the investment, and then uses a deep noise reduction encoder to learn the initial values for potential features of cost and investment effectiveness. A Gaussian radial basis function used to construct a weighted utility function for each uncertainty, generate a minimization of the objective function for the tensor decomposition, and then optimize the objective loss function for the tensor decomposition, find the corresponding weights, and perform noise reduction to generalize the nonlinear problem to evaluate the effectiveness of nuclear power investment. Finally, the two dimensions of cost and risk (estimation of investment value and measurement of investment risk) are applied and simulated through actual data in Kazakhstan.

The authors assess the core indicators of Kazakhstan's nuclear power plants throughout their construction and operating cycles, based on data relating to a cluster of nuclear power plants of 10 different technologies. The authors compared it with several popular methods for evaluating the benefits of nuclear power generation and conducted subsequent sensitivity analyses of key indicators. Experimental results on the dataset show that the MGT method outperforms the other four methods and that changes in nuclear investment returns are more sensitive to changes in costs while operating cash flows from nuclear power are certainly an effective way to drive investment reform in inland nuclear power generation in Kazakhstan at current levels of investment costs.

Future research could consider exploring other excellent methods to improve the accuracy of the investment prediction further using sparseness and noise interference. Also consider collecting some expert advice and providing more appropriate specific suggestions, which will facilitate the application in practice.

The Novel Coronavirus epidemic has plunged the global economy into a deep recession, the tension between China and the US has made the energy cooperation road unusually tortuous, Kazakhstan in Central Asia has natural geographical and resource advantages, so China–Kazakhstan energy cooperation as a new era of opportunity, providing a strong guarantee for China's political and economic stability. The basic idea of building large-scale nuclear power plants in Balkhash and Aktau is put forward, considering the development strategy of building Kazakhstan into a regional international energy base. This work will be a good inspiration for the investment of nuclear generation.

This study solves the problem of increasing noise by combining Monte Carlo simulation with geometric Brownian motion under complex conditions, adds the measure of investment flexibility and strategic value, constructs the utility function of noise reduction weight based on Gaussian radial basis function and extends the nonlinear problem to the evaluation of nuclear power investment benefit.

The purpose of this paper is to develop a time implicit discontinuous Galerkin method for the simulation of two‐dimensional time‐domain electromagnetic wave propagation on non‐uniform triangular meshes.

The proposed method combines an arbitrary high‐order discontinuous Galerkin method for the discretization in space designed on triangular meshes, with a second‐order Cranck‐Nicolson scheme for time integration. At each time step, a multifrontal sparse LU method is used for solving the linear system resulting from the discretization of the TE Maxwell equations.

Despite the computational overhead of the solution of a linear system at each time step, the resulting implicit discontinuous Galerkin time‐domain method allows for a noticeable reduction of the computing time as compared to its explicit counterpart based on a leap‐frog time integration scheme.

The proposed method is useful if the underlying mesh is non‐uniform or locally refined such as when dealing with complex geometric features or with heterogeneous propagation media.

The paper is a first step towards the development of an efficient discontinuous Galerkin method for the simulation of three‐dimensional time‐domain electromagnetic wave propagation on non‐uniform tetrahedral meshes. It yields first insights of the capabilities of implicit time stepping through a detailed numerical assessment of accuracy properties and computational performances.

In the field of high‐frequency computational electromagnetism, the use of implicit time stepping has so far been limited to Cartesian meshes in conjunction with the finite difference time‐domain (FDTD) method (e.g. the alternating direction implicit FDTD method). The paper is the first attempt to combine implicit time stepping with a discontinuous Galerkin discretization method designed on simplex meshes.

This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time.

In a method of lines setting, a meshless method for their discretization in space is proposed. This discretization is based on a DQ approach, and RBFs are used as test functions. A local approach is followed where only selected RBFs feature in the computation of a particular DQ weight.

The proposed method is applied on four reaction-diffusion models: Huxley’s equation, a linear reaction-diffusion system, the Gray–Scott model and the two-dimensional Brusselator model. The method captured the various patterns of the models similar to available in literature. The method shows second order of convergence in space variables and works reliably and efficiently for the problems.

The originality lies in the following facts: A meshless method is proposed for reaction-diffusion models based on local RBFs; the proposed scheme is able to capture patterns of the models for big time T; the scheme has second order of convergence in both time and space variables and Nuemann boundary conditions are easy to implement in this scheme.

The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated.

The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion.

Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state.

A complete investigation of the stabilized formulation of the compressible problem is addressed.

The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem.

The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P₂, P₂, P₁, P₂) to approximate the density, velocity, pressure and temperature field.

The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.