Sharif Digital Repository

In this work, a high-order nodal discontinuous Galerkin method is applied and assessed for the simulation of compressible non-cavitating and cavitating flows. The one-fluid approach with the thermal effects is used to properly model the cavitation phenomenon. Here, the spatial and temporal derivatives in the system of governing equations are discretized using the nodal discontinuous Galerkin method and the third-order TVD Runge–Kutta method, respectively. Various numerical fluxes such as the Roe, Rusanov, HLL, HLLC and AUSM+-up and two discontinuity capturing methods, namely, the generalized MUSCL limiter and a generalized exponential filter are implemented in the solution algorithm. At... 

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free... 

In this paper, an anisotropic weight function in the elliptic form is introduced for the Element Free Galerkin Method (EFGM). In the circular (isotropic) weight function, each node has one characteristic parameter that determines its domain of influence. In the elliptic weight function, each node has three characteristic parameters that are major influence radius, minor influence radius and the direction of the major influence. Using the elliptic weight function each point of the domain may be affected by a less number of nodes in certain conditions. Thus, the computational cost of the method is decreased. In addition, the dependency of the solution on the method that is used for the... 

Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM)... 

This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type (Formula Presented.)▵2u-λM(‖∇u‖2)▵u-μ|x|4u=h(x)uγ+k(x)uα,under Navier boundary conditions, u= ▵u= 0. Here Ω⊂ RN, N≥ 1 is a bounded C4-domain, 0 ∈ Ω, h(x) and k(x) are positive continuous functions, γ∈ (0 , 1) , α∈ (0 , 1) and M: R+→ R+ is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for m0 and 0 < μ< μ∗. Here μ∗=(N(N-4)4)2 is the best constant in the Hardy inequality. Besides, if μ= 0 , λ> 0 and h, k are Lipschitz functions, we show that this problem has a positive smooth... 

In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton's principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam  

In this paper the element free Galerkin method (EFGM) has been extended to be used in the elastoplastic stress analysis. The developed method has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. To do this, at the first step by using the incremental relations of plastic deformation a system of elastoplastic EFGM equations has been derived. Since the obtained relations are nonlinear, a nonlinear solution technique has been chosen. To examine the validity of this technique, stress fields in two different plates with and without a crack have been calculated and the results have been compared with other similar analytical works in the... 

In this paper, we investigate the local and global existence, asymptotic behavior, and blow-up of solutions to the Cauchy problem for Choquard-type equations involving the p(x)-Laplacian operator. As a particular case, we study the following initial value problem [Formula presented] where p,q,V:RN→R and α:RN×RN→R are continuous functions that satisfy some conditions which will be stated later on, and u0:RN→R is the initial function. Under some appropriate conditions, we prove the local and global existence of solutions for the above Cauchy problem by employing the abstract Galerkin approximation. Moreover, the blow-up of solutions and large-time behavior are also investigated. © 2021... 

The discontinuous Galerkin method is used to solve the non-linear spherical shallow water equations with Coriolis force. The numerical method is well-balanced and takes wetting/drying into account. The two fold goal of this work is a comparative study of dynamic and static tsunami generation by seabed displacement and the careful validation of these source models. The numerical results show that the impact of the choice of seabed displacement model can be significant and that using a static approach may result in inaccurate results. For the validation of the studies, we consider measurements from satellites and buoy networks for the 2011 Tohoku event and the 2004 Sumatra–Andaman tsunami. The... 

Dynamic behavior of a laminated composite beam (LCB) supported by a generalized Pasternak-type viscoelastic foundation, subjected to a moving two-degree-of-freedom (DOFs) oscillator with a constant axial velocity is studied. Analytical solution using the Galerkin method is sought and the couplings of the bending-tension, shear-tension, and bending-twist with the Poisson effect are considered. The possible separation of the moving oscillator from LCB during the course of motion is investigated by monitoring the contact force between the oscillator and LCB. The effects of the non-rigid foundation, oscillator parameters, and the load speed on the separation are also studied. It is found that... 

This paper investigates the static and dynamic characteristics of composite thin-walled beams that are constructed from a single-cell box. The structural model considered herein incorporates a number of nonclassical effects, such as material anisotropy, transverse shear, warping inhibition, nonuniform torsional model and rotary inertia. The governing equations were derived using extended Hamilton's principle and solved using extended Galerkin's method. The effects of fiber orientation on static deflection and natural frequencies are considered and a number of important conclusions are outlined. © 2007 Elsevier Ltd. All rights reserved  

In this paper, the large amplitude tree vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton's principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the... 

In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the... 

In this paper, a three-dimensional simulation of fully coupled multiphase fluid flow and heat transfer through deforming porous media is presented in the context of EFG mesh-less method. Spatial discretization of the system of governing equations is performed using EFG and a fully implicit finite difference scheme is employed for temporal discretization. Penalty method is used for imposition of essential boundary conditions. The developed numerical tool is employed to simulate two problems of nuclear waste disposal and CO2 sequestration in deep underground strata. The obtained results demonstrate the capability and robustness of the developed EFG code. © 2018 Elsevier Ltd  

In this study, a high-order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier-Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual-time stepping... 

In this work, a high-order nodal discontinuous Galerkin method (NDGM) is developed and assessed for the simulation of 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several... 

In this study, the nodal discontinuous Galerkin method is formulated in three-dimensions and applied to simulate three-dimensional non-cavitating/cavitating flows. For this aim, the three-dimensional preconditioned Navier-Stokes equations based on the artificial compressibility approach considering appropriate source terms to model cavitating phenomena are used. The spatial derivative terms in the resulting equations are discretized by utilizing the nodal discontinuous Galerkin method on tetrahedral elements and the derivative of the solution vector with respect to the artificial time is discretized by applying an explicit time integration method. An artificial viscosity method is formulated... 

In this paper, a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement field is a superposition of the classical Euler-Bernoulli beam's displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of J-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modified...