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The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by finite element method (FEM).

The semi-implicit stabilization scheme, characteristic-based polynomial pressure projection (CBP3) consists of the Characteristic-Galerkin method and polynomial pressure projection. Theoretically, the proposed scheme works for any type of element using equal-order approximation for velocity and pressure. In this work, linear 3-node triangular and 4-node tetrahedral elements are the focus, which are the simplest but most difficult elements for pressure stabilizations.

The present paper proposes a new scheme, which can stabilize FEM solution for flows of both low and relatively high Reynolds numbers. And the influence of stabilization parameters of the CBP3 scheme has also been investigated.

The research in this work is limited to the laminar incompressible flow.

The verification and validation of the CBP3 scheme are conducted by several 2 D and 3 D numerical examples. The scheme could be used to deal with more practical fluid problems.

The application of scheme to study complex hemodynamics of patient-specific abdominal aortic aneurysm is also presented, which demonstrates its potential to solve bio-flows.

The paper simulated 2 D and 3 D numerical examples with superior results compared to existing results and experiments. The novel CBP3 scheme is verified to be very effective in handling convection and pressure oscillation.

In our earlier papers we have presented a general algorithm for the solution of both compressible and incompressible Navier‐Stokes equations. The objective of the present work is to show the performance of this algorithm when it is used to solve thermal flow problems. Both natural and forced convection and transient problems are considered in this study. The semi‐implicit form of the algorithm has been used to deal with a variety of these problems.

Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.

A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.

The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R²) is 0.93 for the validation set, and the R² for the test set A and test set B are 0.93 and 0.94, respectively.

This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference r_o-r_i. Moreover, several Darcy numbers have been considered.

A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement.

For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number.

A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems.

The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility.

This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

The purpose of this paper is to introduce a local Newton basis functions collocation method for solving the 2D nonlinear coupled Burgers’ equations. It needs less computer storage and flops than the usual global radial basis functions collocation method and also stabilizes the numerical solutions of the convection-dominated equations by using the Newton basis functions.

A meshless method based on spatial trial space spanned by the local Newton basis functions in the “native” Hilbert space of the reproducing kernel is presented. With the selected local sub-clusters of domain nodes, an approximation function is introduced as a sum of weighted local Newton basis functions. Then the collocation approach is used to determine weights. The method leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs).

The method is successfully used for solving the 2D nonlinear coupled Burgers’ equations for reasonably high values of Reynolds number (Re). It is a well-known issue in the analysis of the convection-diffusion problems that the solution becomes oscillatory when the problem becomes convection-dominated if the standard methods are followed without special treatments. In the proposed method, the authors do not detect any instability near the front, hence no technique is needed. The numerical results show that the proposed method is efficient, accurate and stable for flow with reasonably high values of Re.

The authors used more stable basis functions than the standard basis of translated kernels for representing of kernel-based approximants for the numerical solution of partial differential equations (PDEs). The local character of the method, having a well-structured implementation including enforcing the Dirichlet and Neuman boundary conditions, and producing accurate and stable results for flow with reasonably high values of Re for the numerical solution of the 2D nonlinear coupled Burgers’ equations without any special technique are the main values of the paper.

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared.

This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split.

In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.

A comprehensive comparison between three versions of the CBS method is provided for the first time.

Natural convection in porous medium‐fluid interface problems are numerically studied by using the characteristic based split (CBS) algorithm. The finite element method is used to solve the governing generalized porous medium equations. The accuracy of the scheme is estimated by comparing the present predictions for a porous cavity with those results available for the same problem. Two different types of interface problems have been considered. In the first case, the domain is vertically divided into two equal parts, while in the second problem the division is along the horizontal direction. Results obtained from the present investigation are compared extensively with existing experimental and numerical data and they are in good agreement with the available literature. Also present results are smooth along the interface and are without any jumps in the solution.

This paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.

The finite element method (FEM) combined with the characteristic‐based split (CBS) algorithm is used to solve the coupled Navier‐Stokes equations in order to simulate EOFs. The Laplace and Poisson‐Boltzmann equations are solved explicitly a priori to the solution of the fluid dynamic equations. The external electric field and internal potential values are then used to construct the source terms of the fluid dynamics equations.

Proposed methodology works excellently on unstructured meshes for both two‐ and three‐dimensional flow problems. The results obtained for benchmark channel flow problems show an excellent agreement with analytical and experimental data.

The idea of using the FEM and the CBS algorithm to solve the governing equations of EOFs is proposed. This particular method of solving these equations is unprecedented. In addition to benchmark examples, a problem of practical importance is also solved in this paper.

To numerically model forced convection heat transfer over arrays of solder balls.

The characteristic based split (CBS) scheme has been used to solve the incompressible Navier‐Stokes equations on unstructured meshes.

The results show an increase in heat transport with increase in Reynolds numbers. A significant change in heat transfer is also noticed with change in angle of attack.

The presented results will be useful in designing cooling systems for electronic components.

This paper aims to present briefly a unified fractional step method for fluid dynamics, incompressible solid mechanics and heat transfer calculations. The proposed method is demonstrated by solving compressible and incompressible flows, solid mechanics and conjugate heat transfer problems.

The finite element method is used for the spatial discretization of the equations. The fluid dynamics algorithm used is often referred to as the characteristic‐based split scheme.

The proposed method can be employed as a unified approach to fluid dynamics, heat transfer and solid mechanics problems.

The idea of using a unified approach to fluid dynamics and incompressible solid mechanics problems is proposed. The proposed approach will be valuable in complicated engineering problems such as fluid‐structure interaction and problems involving conjugate heat transfer and thermal stresses.