Wajaree Weera¹, Thongchai Botmart^1,*, Samina Zuhra², Zulqurnain Sabir³, Muhammad Asif Zahoor Raja⁴, Salem Ben Said⁵

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 4453-4467, 2023, DOI:10.32604/cmc.2023.033232

Abstract This works intends to provide numerical solutions based on the nonlinear fractional order derivatives of the classical White and Comiskey model (NFD-WCM). The fractional order derivatives have provided authentic and accurate solutions for the NDF-WCM. The solutions of the fractional NFD-WCM are provided using the stochastic computing supervised algorithm named Levenberg-Marquard Backpropagation (LMB) based on neural networks (NNs). This regression approach combines gradient descent and Gauss-Newton iterative methods, which means finding a solution through the sequences of different calculations. WCM is used to demonstrate the heroin epidemics. Heroin has been on-growth world wide, mainly in Asia, Europe, and the USA.… More >

M. J. Huntul^1,*, Taki-Eddine Oussaeif²

Computer Systems Science and Engineering, Vol.40, No.3, pp. 1109-1126, 2022, DOI:10.32604/csse.2022.020175

Abstract In this paper, we consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation whose leading coefficient depends on time variable under nonlocal integral overdetermination condition. We obtain sufficient conditions for the unique solvability of the inverse problem. The existence and uniqueness of the solution of the inverse parabolic problem upon the data are established using the fixed point theorem. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For example, seismology, medicine, fusion welding, continuous casting, metallurgy, aircraft, oil and gas production during drilling and operation… More >

R. Kalaivanan¹, N. Vishnu Ganesh², Qasem M. Al-Mdallal^3,*

FDMP-Fluid Dynamics & Materials Processing, Vol.17, No.2, pp. 319-332, 2021, DOI:10.32604/fdmp.2021.012789

Abstract The buoyancy driven flow of a second-grade nanofluid in the presence of a binary chemical reaction is analyzed in the context of a model based on the balance equations for mass, species concentration, momentum and energy. The elastic properties of the considered fluid are taken into account. The two-dimensional slip flow of such non-Newtonian fluid over a porous flat material which is stretched vertically upwards is considered. The role played by the activation energy is accounted for through an exponent form modified Arrhenius function added to the Buongiorno model for the nanofluid concentration. The effects of thermal radiation are also… More >

V.C. Mariani¹, E.E.M. Alonso², S. Peters³

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.1, pp. 15-28, 2008, DOI:10.3970/cmes.2008.029.015

Abstract An application of Newton's method for linearization of advective terms given by the discretization on unstructured Voronoi meshes for the incompressible Navier-Stokes equations is proposed and evaluated in this article. One of the major advantages of the unstructured approach is its application to very complex geometrical domains and the mesh is adaptable to features of the flow. Moreover, in this work comparisons with the literature results in bi-dimensional lid-driven cavities for different Reynolds numbers allow us to assess the numerical properties of the new proposed finite-volume scheme. Results for the components of the velocity, and the pressure collocated at the… More >

L.N. Gergidis, D. Kourounis, S. Mavratzas, A. Charalambopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 157-176, 2007, DOI:10.3970/cmes.2007.021.157

Abstract A new complete set of scattering eigensolutions of Helmholtz equation in spheroidal geometry is constructed in this paper. It is based on the extension to exterior boundary value problems of the well known Vekua transformation pair, which connects the kernels of Laplace and Helmholtz operators. The derivation of this set is purely analytic. It avoids the implication of the spheroidal wave functions along with their accompanying numerical deficiencies. Using this novel set of eigensolutions, we solve the acoustic scattering problem from a soft acoustic spheroidal scatterer, by expanding the scattered field in terms of it. Two approaches concerning the determination… More >

V. Haslavsky, E. Miroshnichenko, E. Kit, A. Yu. Gelfgat

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.3, pp. 209-234, 2013, DOI:10.3970/fdmp.2013.009.209

Abstract Experimental and numerical observations of oscillatory instability of melt flow in a Czochralski model are compared, and a disagreement observed at small crystal dummy rotation rates is addressed. To exclude uncertainties connected with flow along the free surface, the latter is covered by a no-slip thermally insulating ring. Experiments reveal an appearance of oscillations at temperature differences smaller than the numerically predicted critical ones. At the same time, a steep increase of the oscillations amplitude is observed just beyond the computed threshold values. By increasing the dummy rotation gradually, we are able to qualitatively confirm the numerically predicted flow destabilization.… More >