نشریه روش های عددی در مهندسی
سال چهل و یکم شماره 2 (زمستان 1401)

In the published studies, peridynamics has been used to simulate crack growth in brittle and quasi-brittle materials, simulation of plastic behaviour and solution of differential equations. With such achievements, the  extent of problems which can be solved using peridynamics is growing. Peridynamics was intended to analyze the impact and the wave propagation problems since its introduction. Due to existence of the characteristic length in peridynamics relations, it has been used to solve problems in various scales. Some researchers have also used peridynamics multiphysics models to analyze heat transfer, diffusion and fluid behavior problems. Analyzing the damage growth in composite materials and investigation of geomechanical problems are among other achievements of using peridynamics. In addition to all these cases, application of peridynamics to biological problems has also received attention in recent years. This paper reviews the studies on the applications of peridynamics in the solution of different problems.

Due to the complexity of laboratory studies of crack growth in pore scale, several numerical methods have been used to analyze the porous media problems. These methods have high computational costs for large 3D samples. Therefore, it is important to provide bypath methods to reduce the computational costs. One of these methods is to simulate the crack growth and failure process in 2D, and generalize it to 3D space. In this research, the possibility of using this method  for failure analysis of 3D models and faster estimation of material behavior is investigated. First, models including one crack and one pore were modeled in ABAQUS software, and then generalized to more complex models containing five pores in different arrangements. Crack growth path and tensile strength of 3D models and 2D sections were calculated and compared separately. Also, the 2D sections were first merged into a 3D coordinate plane and finally displayed in 3D space. The results showed that the 2D sections which include the largest number of pores in the 3D model, provide better results. Moreover, the final fracture plane of the sample in 2D sections is the same as the 3D model. The average tensile strength of 2D sections is acceptable compared to 3D models and shows less than 6% difference from the original models in most cases. The close match between 2D and 3D models, as well as reducing the run time of processing to about 85%, is promising and indicates the efficiency of such methods.

Numerical approaches are one of the best tools for seismic response analysis. In between,  the Boundary Element Method (BEM) has attracted special attention. In this paper, a comprehensive study has been performed to characterize the dependence of stability and accuracy of the time domain BEM on the chosen time step duration and effective length of the elements. To this end, the two parameters β and λ/L, widely known and used in the literature for the investigation of numerical stability and accuracy, have been employed. Three different environments as homogeneous, pseudo-homogeneous and non- homogeneous have been analyzed through total number of 280 numerical models. It is found that the stability and accuracy of the used algorithm is considerably influenced by the mentioned parameters, in a way that stable and accurate results will be achieved merely when the wave travels one-fourth to less than half the element size during each time step (0.24<β<0.4) and also when at least one and a half node is defined per the shortest wave-length (λ/L>1.5). It also became clear that in the modeling of non-homogeneous environments, the β value for the environment with the lowest wave velocity specifies the range of acceptable results.

A Modified Single-Level Fast Multipole Method (MSLFMM) for large-scale heat conduction problems is presented. This method is obtained by embedding the far-field approximation (FFA) within the traditional single-level fast multipole method (SLFMM). The FFA is used to compute the influence coefficients of the far elements within adjacent cells, and also to determine the moments of the elements within far cells. This approximation not only reduces the difficulty of procedures and programming, but also causes a significant decrease in the CPU time. Several problems are considered to verify and evaluate the proposed method. The computational cost of the MSLFMM is demonstrated by comparing the Conventional Boundary Element Method (CBEM), the SLFMM, and the Multi-Level Fast Multipole Method (MLFMM). It is shown that the MSLFMM is much faster than the SLFMM, and comparable with the MLFMM due to its ease of use. Finally, to check the ability of the proposed method in modeling a complicated problem, steady-state heat conduction in an engine block is solved. The numerical results show a good agreement with those obtained by a Finite Volume Method (FVM), and its difference is less than 1.5%.

In this paper, nanofluid heat transfer in a microchannel has been studied using homogenous and Buongiorno’s models, and compared with Eulerian-Lagrangian model. The base fluid is water and the particles are Al2O3 and Cu with a diameter of 100nm. The volume fraction is up to 2% and Reynolds number is in the range of 250-1000. The governing equations including continuity, momentum and energy, have been solved using a control volume method (SIMPLE). The results show that for Water-Al2O3, the maximum difference between the homogeneous model and the Eulerian-Lagrangian model is 7.5%, and for Buongiorno’s model is 3%. It can be concluded that the Buongiorno’s model has an acceptable accuracy in results, and is simple enough to be used. On the other hand, unlike the Eulerian-Lagrangian, Buongiorno’s model doesn’t need the parallel processing and super computers, and is a good model to predict heat transfer of nanofluids.

Optimum oil displacement is the most important goal of pre-flush stage during matrix acidizing. In this study, the visco-capillary behavior of the two-phase flow in the pore-scale is analyzed using computational fluid dynamics. A two-dimensional model, based on Cahn–Hilliard phase-field and Navier–Stokes equations, was established and solved using the finite element method. To recognize the effective forces of two-phase flow displacement, a stability phase diagram based on the Logarithm of capillary number (Nc) versus the Logarithm of viscosity ratio (M) was constructed and then compared with the reported experimental data. After identifying both viscous fingering and capillary fingering regions, the most stable displacement region was found to be located at Log M ≈ 0.5 and Log Nc ≈ -2. Furthermore, the impact of four independent variables that critically affect the efficiency of the pre-flush stage, including pore volume of injection (1<PV<5), capillary number (-60.95) occurred at Log M > 0, -4.5 1, and θ> π/6 conditions. It is worth mentioning that for Log M< 0, the optimum condition occurred at Log M ≈ 0, Log Nc ≈ -3.5, PV ≈ 4 and θ ≈ π/6.

Numerical simulation of multiphase problems with complex interface as well as high density ratios is one of the numerical challenges associated with particle scattering and divergence. Fewer problems have been performed with density-based smooth particle hydrodynamics (WCSPH) to solve complex joint surface currents, and most simulations have been performed using Incompressible Smooth Particle Hydrodynamics (ISPH). Solution of high density flows by the smooth particle hydrodynamics is associated with particle dispersion and divergence. Various methods have been used to eliminate the scattering of particles, such as a repulsive force at the interface or the corrected density re-value, but there is a problem of particle disintegration at the interface at higher times. In the present simulation, to simulate multiphase flows with complex surfaces and high density ratios, a new density-based smooth particle hydrodynamics approach has been utilized. To prevent the scattering of particles, especially at the interface at the end times, a simple method with the removal of incompatible particles is used. In the present study, the particle displacement optimization scheme for regularization at the interface of the phase is created by precisely implementing a two-stage change algorithm, so as to maintain the regular particle distribution continuously and conservatively. To examine the accuracy of the present simulation method, it is firstly compared with two-phase Poiseuille flow with three fluids having different values of viscosity, Reynolds-Taylor instability and single bubble rising in a fully filled container., Then it is compared with analytical and numerical solutions. The accuracy and consistency of the current simulation is higher or equal to other simulations.