Volume 15, Issue 2

This paper treats the control of nonstationary oscillations of the pressure which arise in the combustion process of a Rijke tube. The low order model of a nonstationary combustion process in a Rijke tube with multiplicative feedback control function is considered, which is investigated by means of two-DOF coupled van der Pol oscillator. The self-excited oscillations in the combustion process are analysed by means of the Extended Lindstedt-Poincare (EL-P) method with multiple time scales. By applying the EL-P method, it is ascertained, that nonstationary oscillations are almost periodic with amplitude and phase, which are functions of the slow time scale. Without control of the fuel influx, the self excited oscillations can approach limit cycles. By applying the fuel control, the influence of control parameters on the quenching of the self excited oscillations is investigated in a phenomenon of competitive quenching and mutual synchronization with close frequencies and multiple harmonics, respectively.

The synchronization of hyperchaotic systems with strictly different models measuring only output variables is presented. The synchronization of strictly different systems has been studied assuming the knowledge of the system parameters and/or the full knowledge of the systems to be synchronized. Here the synchronization of hyperchaotic systems is presented assuming that only the output system states are available for feedback. The controllers mainly counteract the effect of parametric uncertainties and differences between vector fields. The control actions are given by linearizing control laws and high gain state estimators, in such manner that both hyperchaotic systems are synchronous. Numerical simulation using the Rössler and Chen hyperchaotic systems is used to corroborate the results.

Zonal RANS/LES modelings have received considerable attention over recent years. Especially with the?attached boundary layers that computed using the Reynolds-averaged Navier – Stokes (RANS) equations, and non-equilibrium zones of the flow by large-eddy simulation (LES). Generation eddies from a smooth RANS field of turbulent eddies capable of supporting the Reynolds stresses in the LES zones are one issue that may affect the accuracy of the results of zonal methods. Synthetic turbulence and controlled forcing are used to generate turbulence structures in the LES zones.

Method of lines (MOL) together with radial basis functions (RBFs) is proposed to find the numerical solution of coupled Korteweg-de Vries (KdV) equations, coupled modified Korteweg-de Vries (mKdV) equations and coupled KdV system. The initial-boudary-value problem is reduced to a system of ordinary differential equations. The system is then solved by the fourth order Runge-Kutta method. Numerical examples are given to illustrate practical usefulness of the present approach. The method is efficient and all the examples take very low CPU time. Accuracy of the method is assessed in terms of L ∞ error norm, number of nodal points and time step size. Superiority of the suggested method is shown through comparison with the spectral collocation method.

In this work, by utilizing the modified PLK (Poincare-Lighthill-Kou) method, we studied the propagation of weakly nonlinear waves in a shallow water theory and obtained the Korteweg-deVries (KdV) and the linearized KdV equations with non-homogeneous term as the governing equations of various order terms in the perturbation expansion. The result obtained here is exactly the same with that of Kodama and Taniuti [6], who employed the so-called “re-normalization method”. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is consistent with the results of Demiray [12], wherein the modified reductive perturbation method had been utilized.

A numerical approach is presented for stochastic identification of rigid-poroplastic material model in forming processes. The numerical solutions for deterministic as well as stochastic direct and inverse problems have been described. The inverse problem is solved by the use of gradient based methods and a sensitivity analysis. The proposed direct and inverse formulation describes probabilistic distributions of material data and boundary conditions. Examples of numerical simulations concern a compression of rigid-poroplastic cylindrical specimen with random material parameter as well as poroplastic ring with random boundary conditions. The stochastic solutions are obtained by application of the Monte Carlo method.

It is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we propose a reaction-diffusion Brusselator model from the viewpoint of the Jumarie's modified Riemann-Liouville fractional derivative. Based on the (G′/G)-expansion method, various kinds of exact solutions are obtained. Our results could be used as a starting point for numerical procedures as well.

The space-time conservation element and solution element (CE/SE) scheme has caught many attention in aeroacoustic research community as an alternative numerical strategy for direct aeroacoustic simulation (DAS). As a result of its strict conversation of flow flux in both space and time, the low-order CE/SE scheme possesses excellent non-dissipative characteristics, expedient in calculating low Mach number DAS which requires uniform numerical accuracy to resolve the widely disparate flow and acoustic scales of the problem. In this paper, an attempt of validating a simplified Courant Number Insensitive CE/SE scheme using carefully selected aeroacoustic benchmark problems is reported. Excellent agreement with the benchmark results obtained firmly establishes that CE/SE scheme is a viable scheme for resolving the nonlinear physics of low Mach number aeroacoustic problems.