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The purpose of this paper is to present a computational study to investigate the effects of rectangular cavity design of a piezoelectrically driven micro‐synthetic‐jet actuator on generated flow.

Flow simulations were done using a compressible Navier‐Stokes solver, which is based on finite element method implementation of a characteristic‐based‐split (CBS) algorithm. The algorithm uses arbitrary Lagrangian‐Eulerian formulation, which allows to model oscillation of the synthetic jet's diaphragm in a realistic manner. Since all simulated flows are in the slip‐flow‐regime, a second order slip‐velocity boundary condition was applied along the cavity and orifice walls. Flow simulations were done for micro‐synthetic‐jet configurations with various diaphragm deflections amplitudes, cavity heights, and widths. All of the simulation results were compared with each other and evaluated in terms of the exit jet velocities, slip‐velocities on the orifice wall and instantaneous momentum fluxes at the jet exit.

It is shown that compressibility and rarefaction have important effects on the flow field generated by the micro‐synthetic‐jet actuator. The effect of the geometrical parameters of the cavity to important flow features such slip and phase lag are presented.

The paper reports results of a systematical study of the flow field inside a micro‐scale synthetic‐jet actuator, providing designers of such devices additional information for sizing the cavity within slip flow regime. Furthermore, it is demonstrated that the CBS, together with slip boundary conditions can be successfully used to compute such flows.

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.

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 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.

To improve inviscid compressible flow solution.

A local element‐size calculation procedure in the streamline direction and a local variable smoothing approach are employed to improve inviscid compressible flow solution. The characteristic based split approach is used as basic solution procedure to demonstrate the employed improvements.

Results show that employing the element size in the streamline direction improves the solution accuracy in the transonic flow region. The nodal variable smoothing is very effective below a Mach number of 0.85 and produces results without any spatial oscillations.

This paper fills the gap by suggesting novel procedures to study Mach number range between zero and supersonic flow.

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.

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.

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.