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The purpose of this paper is to focus on modeling buoyancy driven viscous flow and heat transfer through saturated packed pebble‐beds via a set of homogeneous volume‐averaged conservation equations in which local thermal disequilibrium is accounted for.

The local thermal disequilibrium accounted for refers to the solid and liquid phases differing in temperature in a volume‐averaged sense, which is modeled by describing each phase with its own governing equation. The partial differential equations are discretized and solved via a vertex‐centered edge‐based dual‐mesh finite volume algorithm. A compact stencil is used for viscous terms, as this offers improved accuracy compared to the standard finite volume formulation. A locally preconditioned artificial compressibility solution strategy is employed to deal with pressure incompressibility, whilst stabilisation is achieved via a scalar‐valued artificial dissipation scheme.

The developed technology is demonstrated via the solution of natural convective flow inside a heated porous axisymmetric cavity. Predicted results were in general within 10 per cent of experimental measurements.

This is the first instance in which both artificial compressibility and artificial dissipation is employed to model flow through saturated porous materials.

The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.

The semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing.

The study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 × 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation.

This paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.

One‐dimensional pipe network flow analysis can be used in many applications to satisfactorily solve various engineering problems. The paper aims to focus on this.

A hybrid nodal method is detailed, which solves the pressure field prior to the elemental flows, and models both compressible gas and incompressible liquid and gas flows.

The results obtained by the algorithm were verified against a number of published benchmark flow problems. The methodology was found to yield accuracy similar or improved, compared with that of others, while being applicable to both incompressible liquid and compressible gas flows. Convergence performance was found to be similar to other hybrid techniques.

All flows are modelled via a single governing equation set. In the case of incompressible flow, the method is capable of dealing with both constant and variable cross‐sectional area ducts. The latter includes geometrically complex pipes such as sudden expansions.

In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

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.

An area of great interest in current computational fluid dynamics research is that of free-surface modelling (FSM). Semi-implicit pressure-based FSM flow solvers typically involve the solution of a pressure correction equation. The latter being computationally intensive, the purpose of this paper is to involve the implementation and enhancement of an algebraic multigrid (AMG) method for its solution.

All AMG components were implemented via object-oriented C++ in a manner which ensures linear computational scalability and matrix-free storage. The developed technology was evaluated in two- and three-dimensions via application to a dam-break test case.

AMG performance was assessed via comparison of CPU cost to that of several other competitive sparse solvers. The standard AMG implementation proved inferior to other methods in three-dimensions, while the developed Freeze version achieved significant speed-ups and proved to be superior throughout.

A so-called Freeze method was developed to address the computational overhead resulting from the dynamically changing coefficient matrix. The latter involves periodic AMG setup steps in a manner that results in a robust and efficient black-box solver.

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.

This study aims to examine both the population balance approach based on the MUltiple SIze Group (MUSIG) model and the average bubble number density transport equation (ABND) model for 3D, low pressure, gas‐liquid, subcooled boiling, vertical flows. The purpose is to assess the ability of both models to predict the radial profile of void fraction, bubble Sauter mean diameter and interfacial area concentration which characterise subcooled boiling.

Improvement in the ABND model to simulate gas‐liquid bubbly flows with heat transfer was achieved by combining the condensation expression with the gaseous mass transport equation within the CFD commercial code CFX4.4.

Overall, both the ABND model and the MUSIG model provided good results in terms of the above‐mentioned criteria when compared against experimental measurements. However, the ABND model was found to have limitations in predicting high‐subcooled boiling flows due to the lack of bubble size resolution to adequately capture the effect of condensation over a range of bubbles sizes.

It is shown that the ABND model provides an economic alternative to the MUSIG model in terms of complexity and computational time, as long as one is aware of the limitations in simulating high‐subcooling flow regimes.

The aim of this paper is to formulate and analyze thermophoresis effects on mixed convection heat and mass transfer from vertical surfaces embedded in a saturated porous media with variable wall temperature and concentration.

The governing partial differential equations (continuity, momentum, energy, and mass transfer) are written for the vertical surface with variable temperature and mass concentration. Then they are transformed using a set of non‐similarity parameters into dimensionless form and solved using Keller‐box method.

Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increases wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pronounced near pure natural convection heat transfer limit, because this phenomenon is directly temperature gradient‐ or buoyancy forces‐dependent.

The predicted results are restricted only to porous media with small pores due to the adoption of Darcy law as a force balance.

The paper explains the different effect of thermophoresis on forced, natural and mixed convection heat, and mass transfer problems. It is one of the first works that formulates and describes this phenomenon in a porous media. The results of this research are important for scientific researches and design engineers.