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The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer.

The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method.

The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step.

It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer.

The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes.

The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

A software package is developed for the modelling and animation of viscous incompressible fluids. The full time‐dependent Navier‐Stokes equations are used to simulate 2D and 3D incompressible fluid phenomena which include shallow and deep fluid flow, transient dynamic flow, vorticity and splashing in simulated physical environments. The package also allows the inclusion of variously shaped and spaced static or moving obstacles that are fully submerged or penetrate the fluid surface. Stable numerical analysis techniques based on finite‐differences are used for the solution of the Navier‐Stokes equations. To model free‐surface fluids, a technique based on the Marker‐and‐Cell method is presented. Based on the fluid’s pressure and velocities obtained from the solution of the Navier‐Stokes equations this technique allows modelling of the fluid’s free surface either by solving a surface equation of by tracking the motion of marker particles. The latter technique is suitable for visualization of splashing and vorticity. Furthermore, an editing tool is developed for easy definition of a physical‐world which includes obstacles, boundaries and fluid properties such as viscosity, initial velocity and pressure. Using the editor, complex fluid simulations can be performed without prior knowledge of the underlying fluid dynamics equations. Finally, depending on the application fluid rendering techniques are developed using standard Silicon Graphics workstation hardware routines.

This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure.

First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used.

The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh.

To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

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.

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an incompressible smoothed particle hydrodynamics (ISPH) technique. In this technique, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is applied. The paper aims to discuss these issues.

The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions. The solutions represented in temperature, vertical velocity and horizontal velocity have been studied with different values of Rayleigh number Ra parameter (103=Ra=105). In addition, characteristic based scheme in Finite Element Method is introduced for modeling the natural convection in a square cavity.

The results for Rayleigh-Taylor instability and natural convection flow had been compared with the previous researches.

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an ISPH technique. In ISPH method, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is introduced. The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions.

A new numerical method is presented for the simulation of flows of incompressible fluids in plane or axisymmetric flows. Under certain assumptions, the physical domain can be transformed into a rectangular domain. This method can involve free surface flow problems. In Newtonian and non‐Newtonian cases, the relevant equations are non‐linear and the solution is carried out in the transformed domain where the stream lines are parallel straight lines.

This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by incorporating a yield stress below which the fluid is assumed to remain non‐deformable. The Bingham fluid is chosen as a model problem and is considered in detail in the text. The finite element formulation adopted in this work is based on a version of the stabilised finite element method, known as the Galerkin/least‐squares method, originally developed by Hughes and co‐workers. This methodology allows use of low and equal order interpolation of the pressure and velocity fields, thus providing an efficient finite element framework. The Newton‐Raphson method has been chosen for solution of the incremental non‐linear problem arising through the temporal discretisation of the evolution problem. Numerical examples are provided to illustrate the main features of the described methodology.

A computational fluid dynamics (CFD) analysis has been carried out on the aerodynamic and thermal behavior of an incompressible Newtonian fluid having a constant property and flowing turbulently through a two-dimensional horizontal high-performance heat transfer channel with a rectangular cross section. The top surface of the channel was kept at a constant temperature, while it was made sure to maintain the adiabatic condition of the bottom surface. Two obstacles, with different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel; they were fixed to the top and bottom surfaces of the channel in a periodically staggered manner to force vortices to improve the mixing and consequently the heat transfer. The first fin-type obstacle is placed on the heated top channel surface, and the second baffle-type one is placed on the insulated bottom surface. Five different obstacle situations were considered in this study, which are referred as cases FF (flat fin and flat baffle), FVD (flat fin and V-downstream baffle), FVU (flat fin and V-upstream baffle), VVD (V-downstream fin and V-downstream baffle) and VVU (V-Upstream fin and V-upstream baffle).

The flow model is governed by Reynolds-averaged Navier–Stokes equations with the k-epsilon turbulence model and the energy equation. These governing equations are discretized by the finite volume method, in two dimensions, using the commercial CFD software FLUENT software with the Semi Implicit Method for Pressure Linked Equations (SIMPLE) algorithm for handling the pressure-velocity coupling. Air is the test fluid with the flow rate in terms of Reynolds numbers ranging from 12,000 to 32,000.

Important deformations and large recirculation regions were observed in the flow field. A vortex causes a rotary motion inside the flow field, which enhances the mixing by bringing the packets of fluid from the near-wall region of the channel to the bulk and the other way around. The largest value of the axial variations of the Nusselt number and skin friction coefficient is found in the region facing the baffle, while the smallest value is in the region near the fin, for all cases. The thermal enhancement factor (TEF) was also introduced and discussed to assess the performance of the channel for various obstacle situations. It is found that the TEF values are 1.273-1.368, 1.377-1.573, 1.444-1.833, 1.398-1.565 and 1.348-1.592 for FF, FVD, FVU, VVD and VVU respectively, depending on the Re values. In all cases, the TEF was found to be much larger than unity; its maximum value was around 1.833 for FVU at the highest Reynolds number. Therefore, the FVU may be considered as the best geometrical configuration when using the obstacles to improve the heat transfer efficiency inside the channel.

This study can be a real application in the field of shell-and-tube heat exchangers and flat plate solar air collectors.

The purpose of this paper is to implement the numerical analysis based on finite volume method to compare the effects of stress-jump (SJ) and stress-continuity (SC) conditions on flow structure around and through a porous circular cylinder.

In this study, a steady flow of a viscous, incompressible fluid around and through a porous circular cylinder of diameter “D,” using Darcy-Brinkman-Forchheimer’s equation in the porous region, is discussed. The SJ condition proposed by Ochoa-Tapia and Whitaker is applied at the porous-fluid interface and compared with the traditional interfacial condition based on the SC condition in fluid and porous media. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of 1 < Re < 40 and 10-7 < Da < 10-2, respectively, and the porosities are e=0.45, 0.7 and 0.95.

Results show that the SJ condition leads to a much smaller boundary layer within porous medium near the interface as compared to the SC condition. Two interfacial conditions yield similar results with decrease in porosity.

There is no published research in the literature about the effects of important parameters, such as Porosity and Darcy numbers on different fluid-porous interface conditions for a porous cylinder and comparison the effects of SJ and SC conditions on flow structure around and through a porous circular cylinder.

This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model.

The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used.

This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results.

The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow.

The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.