---

A consistent implicit Incompressible Smoothed Particle Hydrodynamics (ISPH) method based on projection approach is proposed for solving violent free surface flow problems. In this way, two consistent discretization schemes are employed for first and second spatial derivatives. In this study, it is shown that in explicit ISPH solvers, the field variables and the positions of particles in the process of numerical differentiation are estimated at two different time steps. So, the incompressibility is not completely satisfied. In the present approach, an iteration loop is implemented, in each time-step. Thus, at the end of each time-step both velocity and the positions used in divergence estimation are at the new time-level. The proposed ISPH method is validated in free surface flow problems involving 2-D dam break benchmarks in which both wet and dry beds are considered. Among the advantages of the present implicit method is being more accurate and stable than the explicit one, despite use of lower number of particles and greater time-step sizes. Also, it provides significant improvement in free surface simulations and pressure distribution results.

---

In this article bubbly flow under the specified axial pressure gradient in a curved channel is studied numerically. To do so, a second order parallelized front-tracking/finite-difference method based on the projection algorithm is implemented to solve the governing equations including the full Navier-Stokes and continuity equations in the cylindrical coordinates system using a uniform staggered grid well fitted to the geometry concerned. In the absence of gravity the mid-plane parallel to the curved duct plane, which is the symmetry plane in the single fluid flow inside the curved duct, separates the bubbly flow into two different flow regions not interacting with each other. Twelve bubbles with diameters of 0.125 wall units are distributed in the equally spaced distances from each other. The numerical results obtained indicate that for the cases studied here, the bubbles reach the statistical steady state with an almost constant final orbital motion path due to the strong secondary field. Furthermore, the effects of different physical parameters such as Reynolds number, and curvature ratio on the flow field at the no slip boundary conditions, are investigated in detail.

---

The interactions between vortical structures and spherical particles or droplets is of practical issues in two-phase flows. The interactions bring major changes in the flow field particularly when coupled with particle rotation. It is observed that the heat transfer rate is significantly influenced during the time that the vortices’ cores are in the vicinity of the particle. In this paper, transient heat transfer of a rotating spherical particle interacting with a pair of vortices in incompressible and viscous flow is studied using numerical solution of the Navier-Stokes and energy equations in the range of 20≥Re≤100 and non-dimensional rotational velocities 0≤Ω≤1, by computational code which has been developed by the authors. In order to ensure the accuracy of the calculation, the results are compared with numerical data reported in the literature and good agreement between results was observed. Then the effect of circulation direction of two vortices interacting with a particle by spin on its heat transfer rate was investigated. Also distribution of heat transfer coefficient at the particle surface with separate rotation around three different axes in two cases of interacting and non-interacting with vortices is given and the results of heat transfer coefficient are presented. The results show that particle rotation for Ω≤0.5, in both presence and absence of vortices in flow field has negligible effects on the particle heat transfer rate; however, with increasing of particle spin significant effects on heat transfer coefficient has been observed that due to the circulation direction of vortices, different amounts are obtained.

---

One of the main difficulties in employing fully coupled algorithms for solving Navier-Stokes equations is the high computation cost of coefficient matrix determination and solving the linear equation system. Therefore, the number of required iterations and computational costs may be reduced by increasing the convergence rate. This article deals with the formulation and testing of an improved fully coupled algorithm based on physical influence scheme (PIS) for the solution of incompressible fluid flow on cell-centred grid. The discretisation of improved algorithm is investigated and fully clarified, by comparing the methodology with two similar schemes. For a better insight, two benchmark problems are solved. The first problem is a steady lid-driven cavity with different Reynolds numbers between 100 and 10000. The second problem is steady flow over a backward facing step for the specified Reynolds number of 800. The history of residuals for present and previous methods are compared, in order to demonstrate the performance of the new discretization scheme. It is worth mentioning, the presented method is based on nine cells discretization. Therefore, the computational costs and memory usage of the proposed method are almost the same as previous ones. The results indicate that, the improved method converges in fewer iterations in comparison with prior methods. The new scheme can be utilized for development of the computational fluid dynamics solvers based on cell-centred grid arrangement.

---