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Articles From Volume - 01 (Issue - 03)
Exponentially-fitted Third-Order Adams-Bashfort Method Paper ID: AJMPA-11-10-2019-135
Abstract : In this paper, the construction of Exponentially-Fitted (EF) versions of the third-order Adam-Bashfort method for oscillatory problems is presented. The convergence and stability properties of the constructed methods are investigated. Numerical experiments confirming the theoretical expectations regarding the constructed methods compared with other standard classical methods are also presented.
Turbulence birth from Poiseuille flow curvature Paper ID: AJMPA-11-10-2019-134
Abstract : In this paper, we considered the well-known parabolic velocity field of Poiseuille flow, as a Riemannian manifold. Calculations of both first and second fundamental forms allowed mean and Gauss curvatures of the paraboloid of revolution, to be calculated. From the Lamb form of Navier-Stokes equation, we calculated both the flexion product and enstrophy giving the Lamb vector divergence as a function of Gauss curvature of the laminar velocity field. These results allowed the stability of Poiseuille flow to be investigated through the influence of maximum flow curvature and the Lamb vector divergence. We showed that classical critical Reynolds number approach is not enough to explain the change from laminar to transition flow regime. A new method, based on Gauss curvature calculation of the Riemannian manifold is then proposed.