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We describe a hybrid method for the solution of hyperbolic conservation laws. A fourth-order total variation diminishing (TVD) finite difference scheme is conjugated with the seven-order WENO scheme. An efficient multi-resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with the… (More)

This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (NavierStocks characteristic boundary conditions) through boundaries is… (More)

- Y Belyaev, Aidarkhan Kaltayev, A Naimanova
- 2010 2nd International Conference on Computer…
- 2010

A computational fluid dynamics code for multispecies, Favre-Averaged Naveir-Stokes equations is developed to simulate the turbulent supersonic two-dimensional reacting flow. The explicit ENO scheme (third order of accuracy) has been used to solve the system of equations, and algebraic Baldwin-Lomax's turbulence model to calculate the eddy viscosity… (More)

In this paper, He’s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial… (More)

- Mohamed Mahmoud Mousa, Aidarkhan Kaltayev, Shahwar F . Ragab
- 2009

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly… (More)

The ultimate goal of this article is to develop a robust and accurate numerical method for solving hyperbolic conservation laws in one and two dimensions. A hybrid numerical method, coupling a cheap fourth order total variation diminishing (TVD) scheme [1] for smooth region and a Robust seventh-order weighted non-oscillatory (WENO) scheme [2] near… (More)

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM… (More)

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