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The purpose of this paper is to develop a coupled approach to solve the pressure–velocity-coupled problem efficiently in the three-dimensional injection molding simulation.

A fully coupled pressure–velocity algorithm is developed to solve the coupled problem, by treating the pressure gradient term implicitly. And, the Schur complement preconditioned FGMRES is applied to decompose the resulting coupled pressure–velocity equation into pressure and velocity subsystems. Then, BoomerAMG is adopted to solve the pressure subsystem, and block Jacobi preconditioned FGMRES is applied to the velocity subsystem.

According to the several experiments, the fully coupled pressure–velocity algorithm was demonstrated to have faster convergence than the traditional SIMPLE algorithm, and the calculating time was reduced by up to 70 per cent. And, the Schur complement preconditioned FGMRES worked more efficiently than block Gauss–Seidel preconditioned FGMRES, block-selective AMG and AMG with block ILU(0) smoother and could take at least 47.4 per cent less time. The proposed solver had good scalability for different-size problems, including various cases with different numbers of elements. It also kept good speedup and efficiency in parallel performance.

A coupled solver has been proposed to effectively solve the coupled problem in the three-dimensional injection molding simulation, which is more robust and efficient than existing methods.

To present conversion of the advection upwind splitting method (AUSM+) from the conventional density‐based and coupled formulation to the pressure‐based and segregated formulation.

The spatial discretization is done by a finite volume method. A collocated grid cell‐center formulation is used. The pressure‐correction procedure is set up in the usual way for a compressible flow problem. The conventional Rhie‐Chow interpolation methodology for the determination of the transporting velocity, and the conventional central interpolation for the pressure at the control volume faces, are replaced by AUSM+ definitions.

The AUSM+ flux definitions are spontaneously well suited for use in a collocated pressure‐correction formulation. The formulation does not require extensions to these flux definitions. As a consequence, the results of a density‐based fully coupled method, are identical to the results of a pressure‐based segregated formulation. The advantage of the pressure‐correction method with respect to the density‐based method, is the higher efficiency for low Mach number applications. The advantage of the AUSM+ flux definition for the transporting velocity with respect to the conventional Rhie‐Chow interpolation, is the improved accuracy in high Mach number flows. As a consequence, the combination of AUSM+ with a pressure‐correction method leads to an algorithm with improved performance for flows at all Mach numbers.

A new methodology, with obvious advantages, is composed by the combination of ingredients from an existing spatial discretization method (AUSM+) and an existing time stepping method (pressure‐correction).

The purpose of this paper is to propose an effective methodology for the industrial design of tangential inlet cyclone separators that is based on the fully three-dimensional (3D) simulation of the flow field within the cyclone coupled with an effective genetic algorithm.

The proposed fully 3D computational fluid dynamics (CFD) model makes use of the Reynold stress model for the accurate prediction of turbulence, while the particle trajectories are simulated using the one-way coupling discrete phase, which is a model particularly effective in case of low concentration of dust. To validate the CFD model, the numerical predictions are compared with experimental data available in the scientific literature. Eight design parameters were chosen, with the two objectives being the minimization of the pressure drop and the maximization of the collection efficiency.

The optimization procedure allows the determination of the Pareto Front, which represents the set of the best geometries and can be instrumental in taking an optimal decision in the presence of such a trade-off between the two conflicting objectives. The comparison among the individuals belonging to the Pareto Front with a more standard cyclone geometry shows that such a CFD global search is very effective.

The proposed procedure is tested for specific values of the operating conditions; however, it has general validity and can be used in place of typical procedures based on empirical models or engineers’ experience for the industrial design of tangential inlet cyclone separators with low solid loading.

Such an optimization process has never been proposed before for the design of cyclone separators; it has been developed with the aim of being both highly accurate and compatible with the industrial design time.

Outlines a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. Considers that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Aims to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end, deals with two well‐known coupled problems of computational mechanics – the fluid‐structure interaction problem and thermally‐driven flows of incompressible fluids. Demonstrates the possibility of coupling the block‐iterative loop with the nonlinearity of the problems through numerical experiments which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. Discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. Explains also the need for online synchronized communication between the different codes used as is the description of the master code which will control the overall algorithm.

The purpose of this paper is to describe a finite element formulation to approximate thermally coupled flows using both the Boussinesq and the low Mach number models with particular emphasis on the numerical implementation of the algorithm developed.

The formulation, that allows us to consider convection dominated problems using equal order interpolation for all the valuables of the problem, is based on the subgrid scale concept. The full Newton linearization strategy gives rise to monolithic treatment of the coupling of variables whereas some fixed point schemes permit the segregated treatment of velocity‐pressure and temperature. A relaxation scheme based on the Armijo rule has also been developed.

A full Newtown linearization turns out to be very efficient for steady‐state problems and very robust when it is combined with a line search strategy. A segregated treatment of velocity‐pressure and temperature happens to be more appropriate for transient problems.

A fractional step scheme, splitting also momentum and continuity equations, could be further analysed.

The results presented in the paper are useful to decide the solution strategy for a given problem.

The numerical implementation of a stabilized finite element approximation of thermally coupled flows is described. The implementation algorithm is developed considering several possibilities for the solution of the discrete nonlinear problem.

The purpose of this paper is to describe two‐ and three‐dimensional numerical modelling of solid oxide fuel cells (SOFCs) by employing an accurate and stable fully matrix inversion free finite element algorithm.

A general and detailed mathematical model has been developed for the description of the coupled complex phenomena occurring in fuel cells. A fully matrix inversion free algorithm, based on the artificial compressibility (AC) version of the characteristic‐based split (CBS) scheme and single domain approach have been successfully employed for the accurate and efficient simulation of high temperature SOFCs.

For the first time, a stable fully explicit algorithm has been applied to detailed multi‐dimensional simulation transport phenomena, coupled to chemical and electrochemical reactions, in fluid, porous and solid parts of a SOFC. The accuracy of the present results has been verified via comparison with experimental and numerical data available in the literature.

For the first time, thanks to a stabilization analysis conducted, the AC‐CBS algorithm has been successfully used to numerically solve the generalized model, applied in this paper to describe transport phenomena through free fluid channels and porous electrodes of SOFCs, without the need of further conditions at the fluid‐electrode interface.

A numerical model is presented for the computation of unsteady two‐fluid interfaces in nonlinear porous media flow. The nonlinear Forchheimer equation is included in the Navier‐Stokes equations for porous media flow. The model is based on capturing the interface on a fixed mesh domain. The zero level set of a pseudo‐concentration function, which defines the interface between the two fluids, is governed by a time‐dependent advection equation. The time‐dependent Navier‐Stokes equations and the advection equation are spatially discretized by the finite element (FE) method. The fully coupled implicit time integration scheme and the explicit forward Eulerian scheme are implemented for the advancement in time. The trapezoidal rule is applied to the fully implicit scheme, while the operator‐splitting algorithm is used for the velocity‐pressure segregation in the explicit scheme. The spatial and time discretizations are stabilized using FE stabilization techniques. Numerical examples of unsteady flow of two‐fluid interfaces in an earth dam are investigated.

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

The results from a direct numerical simulation (DNS) of turbulent, incompressible flow through a square duct, with an imposed temperature difference between the horizontal walls, are presented. The vertical walls are assumed perfectly insulated, and the Reynolds number, based on the bulk velocity and the hydraulic diameter, is about 4400. Our results indicate that secondary motions do not affect dramatically global parameters, like the friction factor and the Nusselt number, with respect to the plane‐channel flow, but the distributions of the local shear stress and heat flux at the walls are highly non‐uniform, due to the presence of these secondary motions. It is also shown that an eddy‐diffusivity approach is capable to reproduce well the turbulent heat flux. All simulations were performed by an efficient finite volume algorithm. A description of the numerical algorithm, together with an analysis of time‐accuracy, is included. The OpenMP parallel programming language was exploited to obtain a moderately‐scalable application.

The suitability of a coupled scheme based on parabolic/elliptic Navier‐Stokes equations for calculating film cooling flows and heat transfer downstream of flush, angled injection slots is explored. The coupled algorithm that combined the coarse mesh ‘outer’ Navier‐Stokes and fine grid ‘inner’ parabolic Navier‐Stokes codes makes retention of the current high resolution model desirable because an acceptable accuracy and economy of computation time are attainable using only mini‐computer resources. The ‘inner‐code’ includes the FLARE approximation to permit small reverse flow. The inner and outer codes are coupled by adopting an approach analogous to classical multigrid methods. It is found that for high blowing mass flow rate of 1.0 with the case of greater than 40° injection angle, the fully parabolic procedure is unable to cope with an extensive separation region immediately downstream of the slot; the present coupling methodology is crucial. The study involves the calculation of heat transfer rates on the surface downstream of the angled slot. Predicted film cooling effectiveness distribution together with the effects of governing parameters are described and show close agreement with the experimental data.