Current Issue : April - June Volume : 2017 Issue Number : 2 Articles : 5 Articles
A simulation was carried out on an unsteady flow of a viscous, incompressible and\nelectrically conducting fluid past an infinite vertical porous plate. A generic computer\nprogram using the Galerkin finite element method is employed to solve the\ncoupled non-linear differential equations for velocity and temperature fields. The\ndiffusion equation, the energy equation, the momentum equations and other relevant\nparameters are transformed into interpretable postfix codes. Numerical calculations\nare carried out on the flow fields both in the presence of cooling and heating of the\nplate by free convection currents. The effects of the dimensionless parameters,\nnamely, the Prandtl number, the Eckert number, the modified Grashof number, the\nSchmidt number and the time on the temperature and velocity distributions are discussed....
A backward differentiation formula (BDF) has been shown to be an effective way to\nsolve a system of ordinary differential equations (ODEs) that have some degree of\nstiffness. However, sometimes, due to high-frequency variations in the external time\nseries of boundary conditions, a small time-step is required to solve the ODE system\nthroughout the entire simulation period, which can lead to a high computational\ncost, slower response, and need for more memory resources. One possible strategy to\novercome this problem is to dynamically adjust the time-step with respect to the system�s\nstiffness. Therefore, small time-steps can be applied when needed, and larger\ntime-steps can be used when allowable. This paper presents a new algorithm for adjusting\nthe dynamic time-step based on a BDF discretization method. The parameters\nused to dynamically adjust the size of the time-step can be optimally specified to\nresult in a minimum computation time and reasonable accuracy for a particular case\nof ODEs. The proposed algorithm was applied to solve the system of ODEs obtained\nfrom an activated sludge model (ASM) for biological wastewater treatment processes.\nThe algorithm was tested for various solver parameters, and the optimum set of three\nadjustable parameters that represented minimum computation time was identified.\nIn addition, the accuracy of the algorithm was evaluated for various sets of solver\nparameters....
A charming feature of symplectic geometry is that it is at the crossroad of many other\nmathematical disciplines. In this article we review the basic notions with examples\nof symplectic structures and show the connections of symplectic geometry with the\nvarious branches of differential geometry using important theorems....
The modeling and solving a transcendental eigenvalue problem are important issues in the transfer matrix method for\nlinear multibody systems. Based on the recursive eigenvalue search algorithm for transfer matrix method for linear multibody\nsystem, the distributed parallel approach for assembling overall transfer matrix and searching eigenvalues is proposed.\nThis is achieved based on Message Parallel Interface. The influence of the CPU core number as well as the\ndistributed network environment on the final computational time is analyzed through numerical examples of both a nonuniform\nbeam and a multiple launch rocket system. The results indicate that the computational time is significantly\nreduced by the proposed parallel computing method, so that the computational efficiency on optimization and design of\ncomplex multibody systems can be improved....
Focusing on the failure under the condition of target blocking, the similarity between\ntarget color and background color for the Camshift algorithm, an improved algorithm\nbased on Camshift algorithm is proposed. Gaussian mixture model is used to\ndetermine the tracking area fast and accurately because it is not sensitive to the external\nconditions such as light and shadow. Kalman predictor is used to predict the\nblocked target effectively. The video is processed in the MATLAB environment. The\nmoving target can be tracked and its position can be predicted accurately with the\nproposed improved algorithm. The results verify the feasibility and effectiveness of\nthe algorithm....
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