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This study aims at developing a comprehensive model for the analysis of electro-osmotic flow (EOF) through a fluid-saturated porous medium. To fully understand and exploit a number of applications, such a model for EOF through porous media is essential.

The proposed model is based on a generalised set of governing equations used for modelling flow through fluid saturated porous media. These equations are modified to incorporate appropriate modifications to represent electro-osmosis (EO). The model is solved through the finite element method (FEM). The validity of the proposed numerical model is demonstrated by comparing the numerical results of internal potential and velocity distribution with corresponding analytical expressions. The model introduced is also used to carry out a sensitivity analysis of the main parameters that control EOF.

The analysis carried out confirms that EO in free channels without porous obstruction is effective only at small scales, as largely discussed in the available literature. Using porous media makes EO independent of the channel scale. Indeed, as the channel size increases, the presence of the charged porous medium is essential to induce fluid flow. Moreover, results demonstrate that flow is significantly affected by the characteristics of the porous medium, such as particle size, and by the zeta potential acting on the charged surfaces.

To the best of the authors’ knowledge, a comprehensive FEM model, based on the generalised equations to simulate EOF in porous media, is proposed here for the first time.

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.

In the present work, a novel dual time stepping approach is applied to a quasi-implicit (QI) fractional step method and its performance is assessed against the classical versions of the QI procedure for the solution of incompressible Navier-Stokes equations. The paper aims to discuss these issues.

In the proposed method, a local time stepping algorithm is utilised to accelerate the solution to steady state, while the transient solution is recovered through the use of a dual time step. It is demonstrated that, unlike the classical fractional step method, the temporal convergence rate of the proposed method depends solely upon the choice of the time discretisation.

While additional stabilisation is the prerequisite for obtaining higher order accuracy in the standard QI methods, the proposed dual time stepping approach completely eliminates this requirement. In addition, the dual time stepping approach proposed achieves the correct formal accuracy in time for both velocity and pressure. It is also demonstrated that a time accuracy beyond second order for both pressure and velocity is possible. In summary, the proposed dual time approach to QI methods simplifies the algorithm, accelerates solution and achieves a higher order time accuracy.

The dual time stepping removed first order pressure error.

The purpose of this paper is to numerically study blood flow through a subject‐specific carotid artery with a moderately severe stenosis, also to thoroughly analyse the wall shear stress (WSS), oscillatory shear index (OSI) and WSS angular deviation (WSSAD). One of the important aspects of this study is the investigation on the influence of the extensions attached to the domain outlets.

The segmentation of the carotid artery is carried out using a deformable model based on a level set method. A geometric potential force (GPF) is employed to deform the level set to obtain the carotid artery geometry. The initial surface meshing is generated using an advanced marching cubes (MC) method, before improving the quality of the surface mesh via a number of mesh cosmetic steps. The volume mesh generation has two parts. In the first part, a quasi‐structured, boundary layer mesh is generated in the vicinity of the geometry walls. The second part of the meshing involves unstructured tetrahedral meshing of the inner part of the geometry. After the meshing stage, the flow boundary conditions are generated by numerically solving the Helmholtz equation in both space and time. Finally, the explicit characteristic‐based split (CBS) method is employed in a parallel environment to produce a detailed analysis of wall quantities.

In general, WSS is very high in the vicinity of the carotid artery apex and in the proximity of the stenosis. From the results obtained, it is clear that the influence of outlet domain extension is marginal. While the peak instantaneous WSS differs by a maximum of 5.7 per cent, the time‐averaged WSS difference due to extended domain is only 1.3 per cent. Two other derived parameters are also examined in the paper, the oscillating shear index and the WSSAD. Both these quantities also display minor or negligible differences due to domain extension.

It has been perceived that domain extension is essential to avoid wrong application of boundary conditions. The results obtained, however, conclusively show that the outlet domain extension has only a moderate influence on WSS. Thus, outlet extension to the domains may not be essential for arterial blood flows. It is also observed that the dramatic values of peak WSS obtained near the stenosis is the result of high resolution mesh along with boundary layers used in this study. Both the outcomes represent the originality of this paper.

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.

This paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media.

Modelling electro-osmosis in fluid systems without solid particles has been first introduced. Then, after a brief description of the existing approaches for porous media modelling, electro-osmotic flow in porous media has been considered by analysing the main contributions to the development of this topic.

The analysis of literature has highlighted the absence of a universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used.

For the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed to provide detailed indications for future works concerning this topic.

In this paper, microscopic and macroscopic approaches to the solution of natural convection in enclosures filled with fluid saturated porous media are investigated. At the microscopic level, the porous medium is represented by different assemblies of cylinders and the Navier‐Stokes equations are assumed to govern the flow. To represent the flow in a macroscopic porous medium approach, the generalised flow model is employed. The characteristic based split scheme is used to solve the conservation equations of both approaches. In addition to the comparison between microscopic and macroscopic approaches of fluid saturated porous enclosures, cavities with interface between fluid saturated porous medium and single phase fluid are also investigated.

The purpose of this paper is to compare the fluid dynamic performance of two Aqueous Humor (AH) ocular drainage devices, the SOLX® Gold Micro Shunt (GMS) and the novel Silicon Shunt Device (SSD), implanted by surgeons in human eyes to reduce the IntraOcular Pressure towards physiological values, by draining the AH from the Anterior Chamber to the Suprachoroidal Space, to cure eyes with glaucoma.

The generalized porous medium model is solved to simulate the AH flow through the two ocular drainage devices and the surrounding porous tissues of the eye.

In the GMS, probable stagnation regions have been found, due to the very small AH velocity values inside the device and to the surrounding tissues, creating possible blockage and malfunction of the device. The simple microtubular geometry of the novel SSD allows to have a regular AH flow and to choose shunts with different diameters and/or with the presence of radial holes, based on patient needs, with consequent reduction of post-operative complications.

The present model will be further developed taking into account the insertion of the present drainage devices inside the anterior section of the eye. The present results show the comparative fluid dynamic performance of the two shunts considered, and can be useful for surgeons to choose the adequate shunt, based on the required AH flow rate for a specific patient.

The present numerical approach, employing the generalized porous medium model, represents a useful tool to study the fluid dynamics of ocular drainage devices and to design these shunts, to reduce post-operative complications.

The generalized porous medium model is here applied for the first time to simulate the interaction of ocular drainage devices with the surrounding porous tissues of the eye.

A comparative study has been carried out to investigate the performance of two different time stepping schemes for convective heat transfer and flow in a fluid saturated porous medium. Both the schemes are based on the velocity correction procedure. The first scheme is a semi‐implicit one in which the linear and non‐linear porous medium terms of the momentum equation are treated implicitly but solution of the simultaneous equation system is avoided by lumping the mass. The second procedure (quasi‐implicit) treats the porous medium and viscous terms implicitly and a simultaneous equation system is constructed to solve the equations of momentum conservation. Two numerical examples have been considered and both the schemes are tested for various parameters governing the flow and heat transfer in these problems. Results show that, at smaller Rayleigh numbers and on fine meshes, the quasi‐implicit scheme gives faster convergence to steady state in both Darcy and non‐Darcy regimes than that of the semi‐implicit scheme. At higher Rayleigh numbers, the semi‐implicit scheme is faster in the Darcy regime. Also, the semi‐implicit scheme is faster than that of the quasi‐implicit scheme on a coarse mesh used in this study. In general both the schemes predict transient cyclic developments well.

The purpose of this paper is to devise a tool based on computational fluid dynamics (CFD) and machine learning (ML), for the assessment of potential airborne microbial transmission in enclosed spaces. A gated recurrent units neural network (GRU-NN) is presented to learn and predict the behaviour of droplets expelled through breaths via particle tracking data sets.

A computational methodology is used for investigating how infectious particles that originated in one location are transported by air and spread throughout a room. High-fidelity prediction of indoor airflow is obtained by means of an in-house parallel CFD solver, which uses a one equation Spalart–Allmaras turbulence model. Several flow scenarios are considered by varying different ventilation conditions and source locations. The CFD model is used for computing the trajectories of the particles emitted by human breath. The numerical results are used for the ML training.

In this work, it is shown that the developed ML model, based on the GRU-NN, can accurately predict the airborne particle movement across an indoor environment for different vent operation conditions and source locations. The numerical results in this paper prove that the presented methodology is able to provide accurate predictions of the time evolution of particle distribution at different locations of the enclosed space.

This study paves the way for the development of efficient and reliable tools for predicting virus airborne movement under different ventilation conditions and different human positions within an indoor environment, potentially leading to the new design. A parametric study is carried out to evaluate the impact of system settings on time variation particles emitted by human breath within the space considered.