Computational Methods in Engineering

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Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in the dissipation term by its constant spectral radius. The objective of the present study is to develop a modified implicit solver based on Roe scheme so that its numerical dissipation is as much as the explicit one. In the proposed scheme, the Krylov subspace method with a LU decomposition preconditioner (GMRES+LU-SGS) is used to solve the linear systems. The efficiency of this method is shown by presenting some examples at the end.

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The main objective of the present study is to utilize a novel linearization strategy to linearize the convection terms of the quasi-one-dimensional Euler governing equations on collocated grids and to examine its shock-capturing capabilities. To avoid a pressure checkerboard problem on the collocated grids, it is necessary to utilize two velocity definitions at each cell face. Similarly, we define two velocity expressions at cell faces known as convecting and convected velocities. We derive them from the proper combinations of continuity and momentum equations which, in turn, provide a strong coupling among the Euler discretized equations. To achieve this, we utilize an advanced linearization strategy known as Newton-Raphson to linearize the nonlinear convection terms. The key point in this linearization is to preserve the original physics behind the two velocities in the linearization procedure. The performance of the new formulation is then investigated in a converging-diverging nozzle flow. The results show great improvement in both the performance of the original formulation and in capturing shocks. The results also indicate that the new extended formulation is robust enough to be used as an all-speed flow solver.

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Among the adaptive-grid methods, redistribution and embedding techniques have been the focus of more attention by researchers. Simultaneous or combined adaptive techniques have also been used. This paper describes a combination of adaptive-grid embedding and redistribution methods on semi-structured grids for two-dimensional invisid flows. Since the grid is semi-structured, it is possible to use different algorithms for combining adaptive-grid embedding and redistribution methods. To evaluate the accuracy and efficiency of the method, this combination is used to solve two model problems, transonic and supersonic inviscid flows in channels with circular arc bump. The results show that combination of adaptive-grid embedding and redistribution methods on semi-structured grids remarkably increases the accuracy at the cost of a slight increase in computational time in comparison with the embedding method alone.

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In the present paper thecompressibleflowoftheunderwaterexplosionhasbeensimulatedusing One-fluid
method along with the Eulerian-Lagrangian ALE method. Besides, the exact Riemann solver and an appropriate
equation of state which is consistent with the thermodynamic behavior of water in underwater explosion, is employed.
The two dimensional underwater explosion problem near a flat plate is modeled. In order to increase the accuracy of
the method for simulating the wave front, the adaptive grid is used. The simulated underwater explosion results
agreed well with other similar numerical simulations. The numerical results indicate the capability of the present
study in simulating the physics of underwater explosion and modeling the fluctuations of explosive bubble and also
predicting the creation and collapse of the caviation zone.

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Wave-field extrapolation based on solving the wave equation is an important step in seismic modeling and needs a high level of accuracy. It has been implemented through a various numerical methods such as finite difference method as the most popular and conventional one. Moreover, the main drawbacks of the finite difference method are the low level of accuracy and the numerical dispersion for large time intervals (∆t). On the other hand, the symplectic integrators due to their structure can cope with this problem and act more accurately in comparison to the finite difference method. They reduce the computation cost and do not face numerical dispersion when time interval is increased. Therefore, the aim of the current paper is to present a symplectic integrator for wave-field extrapolation using the Euler method. Then, the extrapolation is implemented  for rather large time intervals using a simple geological model. The extrapolation employed for both symplectic Euler and finite difference methods showed a better quality image for the proposed method. Finally the accuracy was compared to the finite difference method
 

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Accurate determination of the response of structures under dynamic loads such as earthquake loads plays an important role in the safe and economical design of structures. The purpose of this paper is to utilize a novel solution method based on the use of exponential basis functions for dynamic analysis of Bernoulli beam subjected to different types of base excitations. This method was firstly introduced for solving scalar wave propagation problems, named as stepwise time-weighted residual method. The proposed method considers the solution as a series of exponential basis functions with unknown constant coefficients; and the problem is solved in time without the need for spatial discretization of the beam and by using an appropriate recursive relation to correct the coefficients of the exponential bases. In order to apply the earthquake excitation, first by using the central finite difference relation, the earthquake acceleration history is converted to displacement history. Moreover, the displacement history is applied to the beam as a time-varying boundary condition. In this study, the capabilities of the proposed method in solving several sample problems of vibration of single and multi-span beams under various stimuli such as earthquake acceleration variations are compared with the results of other existing methods.

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Accurate modeling of fluidization and heat transfer phenomena in gas-solid fluidized beds is not solely dependent  on the particular selected numerical model and involved algorithms. In fact, choosing the right model for each specific operating condition, the correct implementation of each model, and the right choice of parameters and boundary conditions, determine the accuracy of the results in the evaluation of the performance of fluidized beds. In this research, in order to accurately simulate heat transfer in fluidized beds, important and effective parameters on two-fluid Eulerian model that incorporate the kinetic theory of granular flow were investigated. For this purpose, effects of particle-particle and particle-wall restitution coefficient, specularity coefficient, granular temperature and effective thermal conductivity coefficients determination methods on the numerical solution were evaluated. These investigations were first carried out on heat transfer from hot air to solid particles in an adiabatic fluidized bed, and then on a fluidized bed with constant temperature walls for bubbling and turbulent regimes. Results showed that specularity coefficient and effective thermal conductivity are important parameters in heat transfer process from wall to bed. In this case, the zero value of the specularity coefficient causes the air temperature to increase by about 7 degrees in the bubbling regime and about 5 degrees in the turbulent regime, and its unit value gives the same results with the no-slip condition. In addition, considering the solid and gas material thermal conductivities causes the outlet air temperature to be about 26 degrees higher than the temperature that is obtained by considering the effective thermal conductivity coefficients with standard approach. The partial differential and algebraic form of the conservation equation for the particles kinetic energy show identical results in dense fluidized beds, although considering a constant granular temperature can cause computational errors.