An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method

Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner-Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. We also present the comparison of this work with numerical results and show that the present method is applicable.Comment: 15 pages, 4 figures; Published online in the journal of "Communications in Nonlinear Science and Numerical Simulation

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications

Centrifugal compressor return channel shape optimization using adjoint method

Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 59-60).This thesis describes the construction of an automated gradient-based optimization process using the adjoint method and its application to centrifugal compressor return channel loss reduction. A proper objective function definition and a generalized geometry parametrization and manipulation algorithm were developed, and the appropriate adjoint equations and boundary conditions were derived for internal flow of an axisymmetric incompressible laminar flow. The adjoint-based gradient calculation was then validated against finite-difference calculations and embedded in a quasi- Newton optimization algorithm. An optimal design was proposed, which achieved an approximately 5% performance improvement compared to the baseline design in an incompressible laminar flow. The geometry was assessed in a compressible turbulent flow at the actual Mach number and Reynolds number and found to yield a 11% performance improvement for an axisymmetric channel with a previously optimized geometry.by Wei Guo.S.M

Growth factor in f(T) gravity

We derive the evolution equation of growth factor for the matter over-dense perturbation in $f(T)$ gravity. For instance, we investigate its behavior in power law model at small redshift and compare it to the prediction of $\Lambda$CDM and dark energy with the same equation of state in the framework of Einstein general relativity. We find that the perturbation in $f(T)$ gravity grows slower than that in Einstein general relativity if \p f/\p T>0 due to the effectively weakened gravity.Comment: 15 pages,1 figure; v2,typos corrected; v3, discussions added, accepted by JCA