Sharif Digital Repository

In this paper, the transient growth of a spherical micro-void under remote thermal load in an infinite medium is investigated. After developing the governing equations in the problem domain, the coupled nonlinear set of equations is solved through a numerical scheme. It is shown that a small cavity can grow rapidly as the temperature increases in a remote distance and may damage the material containing preexisting micro-voids. Conducting a transient thermal analysis simultaneously with a structural one reveals that the material may experience a peak in the radial stress distribution, which is five times larger compared to the steady-state one, and shows the importance of employing a... 

Stochastic differential equations (SDE) play an important role in a range of application areas, including biology, physics, chemistry, epidemiology, mechanics, microelectronics, economics, and finance [1]. However, most SDEs, especially nonlinear SDEs, do not have analytical solutions, so that one must resort to numerical approximation schemes in order to simulate trajectories of the solutions to the given equation. The simplest effective computational method for approximation of ordinary differential equations is the Euler’s method. The Euler–Maruyama method is the analogue of the Euler’s method for ordinary differential equations for numerical simulation of the SDEs [2]. Another numerical... 

Stochastic differential equations (SDE) play an important role in a range of application areas, including biology, physics, chemistry, epidemiology, mechanics, microelectronics, economics, and finance [1]. However, most SDEs, especially nonlinear SDEs, do not have analytical solutions, so that one must resort to numerical approximation schemes in order to simulate trajectories of the solutions to the given equation. The simplest effective computational method for approximation of ordinary differential equations is the Euler’s method. The Euler–Maruyama method is the analogue of the Euler’s method for ordinary differential equations for numerical simulation of the SDEs [2]. Another numerical... 

Hybrid FVM-LBM schemes are developed in the past few years to use capabilities of both Navier-Stokes based finite volume method (FVM) and lattice Boltzmann method (LBM) to solve macro-meso multiscale problems. In this scheme, the major task is to develop some lifting relations that reconstruct distribution functions in LBM sub-domain from macroscopic variables and their derivatives. The macroscopic variables are computed using Navier-Stokes based FVM in macroscale sub-domain, while distribution functions are computed using LBM in mesoscale sub-domain. The pioneer works in this area used the single relaxation time (SRT) version of LBM. However, it is known that the numerical stability and... 

In this paper, a transient-dynamic analysis is presented for large deformation of powder forming process. The technique is employed using the contact friction algorithm and plasticity behavior of powder. The contact algorithm is applied by imposing the contact constraints and modifying the contact properties of frictional slip through the node-to-surface contact algorithm. A double-surface cap plasticity model is used for highly nonlinear behavior of powder. In order to predict the non-uniform density and stress distributions during powder die-pressing, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components  

The asymmetric problem of lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space is addressed. With the aid of appropriate Green's functions, the governing equations of the problem are written as a set of coupled integral equations. With further mathematical transformations, the system of dual integral equations is reduced to two coupled Fredholm integral equations of the second kind which are amenable to numerical treatments. The exact closed-form solutions corresponding to two limiting cases of a membrane resting on the surface of a half-space and embedded in a full-space are derived. The jump behavior of results at the edge of the membrane... 

In this paper, the dynamic modeling of powder compaction processes is presented based on a simple contact algorithm to evaluate the distribution of final density in dynamic powder die-pressing. The large deformation frictional contact is employed by imposing the contact constraints via the contact node-to-surface formulation and modifying the contact properties of frictional slip. The Coulomb friction law is used to simulate the friction between the rigid punch and the work-piece. The nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large FE deformation in order to predict the non-uniform relative density... 

In this paper, the three-dimensional large frictional contact deformation of powder forming process is modeled using a node-to-surface contact algorithm based on the penalty and augmented-Lagrange approaches. The technique is applied by imposing the normal and tangential contact constraints and modifying the contact properties of frictional slip. The Coulomb friction law is employed to simulate the friction between the rigid punch and the work piece. It is shown that the augmented-Lagrange technique significantly improves imposing of the constraints on contact surfaces. In order to predict the non-uniform relative density and stress distributions during the large deformation of powder... 

By virtue of a complete set of displacement potential functions and Hankel transform, the analytical expressions of Green's function of an exponentially graded elastic transversely isotropic half-space is presented. The given solution is analytically in exact agreement with the existing solution for a homogeneous transversely isotropic half-space. Employing a robust asymptotic decomposition technique, the Green's function is decomposed to the closed-form Green's function corresponding to the homogeneous transversely isotropic half-space and grading term with strong decaying integrands. This representation is very useful for numerical methods which are based on boundary-integral formulations... 

Particle dispersion in the vortex flow has been one of the most interesting subjects in recent years. Bidirectional vortex flow field is an industrial sample of rotating flow which is used to obtain advantages of better mixing and combustion. In this work penetration and dispersion quality of particles which are entering from various positions on the vortex engine walls have been numerically predicted. Head side, end side, and sidewall are considered as the entering positions. The particle has been assumed to be a rigid sphere. Initial velocity, diameter, and density of entering particles are assumed to be known. If the particle length scale is considered not to be comparable with the... 

This paper presents a numerical scheme for stability analysis of the aeroelastic systems in the Laplace domain. The proposed technique, which is called the PP method, is proposed for when the aerodynamic model is represented in the Laplace domain and includes complicated transcendental expressions in terms of the Laplace variable. This method utilizes a matrix iterative procedure to find the eigenvalues of the system and generalizes the other methods such as the P and PK methods for prediction of the flutter conditions. The major advantage of this technique over the other approximate methods is true prediction of subcritical damping and frequency values of the aeroelastic modes. To examine... 

Purpose - This paper aims to perform a comparative study between capabilities of two numerical schemes from two main branches of numerical methods for solving hyperbolic conservation equations. Design/methodology/ approach - The accuracy and performance of a newly developed high-resolution central scheme vs a higher-order Godunov-based method are evaluated in the context of black-oil reservoir simulations. Both methods are modified enabling study of applications that are not strictly hyperbolic and exhibit local linear degeneracies in their wave structure. Findings - The numerical computations show that while both schemes produce results with virtually the same accuracy, the Godunov method... 

General purpose software is developed to simulate 6-DoF fluid-structure interaction in two-phase viscous flow. It is a VoF-fractional step solver based on the finite-volume discretization which uses a boundary-fitted body-attached hexahedral grid as the motion simulation strategy. As an application, a high-speed planing catamaran is simulated in steady forward motion as well as in turning maneuver. Results are compared with the available data and good qualitative and quantitative agreements are achieved. Numerical schemes and the solution algorithm of the software are consistent and show a good capability to model highly nonlinear ship motions. It can be further developed to represent a more... 

A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers' equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities, comparison with the results obtained using other numerical schemes... 

The dynamic behavior of a functionally graded (FG) simply supported Euler-Bernoulli beam subjected to a moving oscillator has been investigated in this paper. The Young's modulus and the mass density of the FG beam vary continuously in the thickness direction according to the power-law model. The system of equations of motion is derived by using Hamilton's principle. By employing Petrov-Galerkin method, the system of fourth-order partial differential equations of motion has been reduced to a system of second-order ordinary differential equations. The resulting equations are solved using Runge-Kutta numerical scheme. In this study, the effect of the various parameters such as power-law... 

This paper uses a fourth-order compact finite-difference scheme for solving steady incompressible flows. The high-order compact method applied is an alternating direction implicit operator scheme, which has been used by Ekaterinaris for computing two-dimensional compressible flows. Herein, this numerical scheme is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. For space discretizing the convective fluxes, fourth-order centered spatial accuracy of the implicit operators is efficiently obtained by performing compact space differentiation in which the method uses block-tridiagonal... 

Kinetic theory based numerical scheme such as direct simulation Monte Carlo (DSMC) and information preservation (IP) schemes properly solve micro-nano flow problems in transition and free molecular regimes. However, the high computational cost of these methods encourages the researchers toward extending the applicability of the continuumbased equations beyond the slip flow regime. In addition to correct velocity profile, the continuum-based equations should predict accurate mass flow rate magnitude. The secondorder velocity slip models derived from the kinetic theory provide accurate velocity profiles up to Kn=0.5; however, they yield erroneous mass flow rate magnitudes because the basic... 

The kinetic-theory-based numerical schemes, such as direct simulation Monte Carlo (DSMC) and information preservation (IP), can be readily used to solve transition flow regimes. However, their high computational cost still promotes the researchers to extend the Navier-Stokes (NS) equations beyond the slip flow and to the transition regime applications. Evidently, a suitable extension would accurately predict both the local velocity profiles and the mass flow rate magnitude as well as the streamwise pressure distribution. The second-order slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its... 

The unsteady flow of blood through stenosed artery, driven by an oscillatory pressure gradient, is studied. An appropriate shape of the time-dependent stenoses which are overlapped in the realm of the formation of arterial narrowing is constructed mathematically. A msathematical model is developed by treating blood as a non-Newtonian fluid characterized by the Oldroyd-B and Cross models. A numerical scheme has been used to solve the unsteady nonlinear Navier-stokes equations in cylindrical coordinate system governing flow, assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. Finite difference technique was used to investigate the...