We present an approach for determining the linear stability of steady-states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady-state solution leads to an eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation. The Cayley transformation requires the...

This work focuses on the a posteriori error estimation for the reduced basis method applied to partial differential equations with quadratic nonlinearity and affine parameter dependence. We rely on natural norms—local parameter-dependent norms—to provide a sharp and computable lower bound of the inf-sup constant. We prove a formulation of the Brezzi–Rappaz–Raviart existence and uniqueness theor...

Abstract. Natural convection heat transfer in a square cavity induced by heated plate is studied numerically. Top and bottom of the cavity are adiabatic, the two vertical walls of the cavity have constant temperature lower than the plate’s temperature. The flow is assumed to be two-dimensional. The discretized equations were solved by finite difference method using Alternating Direction Implici...

In this work, mixed convection from an inclined square cylinder in a cavity is numerically investigated. A commercial CFD solver Ansys Fluent used to solve the problem. First, located at center of cavity, then location changed along x-axis. The walls are assumed be adiabatic and isothermal boundary condition. Reynolds number, Re varies 100 300 Grashof numbers, Gr range 103 105 throughout work. ...

In this paper, Turbulent mixed convective heat transfer of water and Al2O3 nanofluid has been numerically studied in a horizontal tube under non-uniform heat flux on the upper wall and insulation in the lower wall using mixture model. For the discretization of governing equations, the second-order upstream difference scheme and finite volume method were used. The coupling of pressure and veloci...

Due to the importance of wall shear stress effect and dust fluid in daily life problems. This paper aims discover influence on fluids fluctuating flow. The flow is considered between two parallel plates that are non-conducting. transformation heat, generated. We consider every particle having spherical uniformly disperse base fluid. perturb solution obtained by applying Poincare-Lighthill pertu...

The effects of radiative heat transfer on the fully developed free convection flow of a viscous incompressible fluid-saturated porous medium between two vertical walls in the presence of a uniform gravitational field have been studied. An exact solution of the governing equations has been obtained. Radiation is found to have significant effects on the velocity field and temperature distribution...

The onset of convection in a three-layer system consisting of two fluid-saturated porous layers separated by a homogeneous fluid layer is studied. It is shown that both a longwave convective regime developing in the whole system and a finite-wavelength regime of convection concentrated in the homogeneous fluid layer are possible. Due to the hydraulic resistance of the porous matrix, the flow in...

The present work is devoted to study a viscous, incompressible, and electrically conducting fluid on an MHD flowing past semi-infinite porous plate in the presence of chemical reaction inclined magnetic parameter. governing equations are expressed non-dimensional form resulting nonlinear solved employing Homotopy perturbation method for nondimensional velocity, temperature, concentration profil...

Explicit Finite-Difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which obtained from the non-linear partial differential equations. These equations describe the twodimensional flow of a MHD third-order Nano-fluid with heat and mass transfer in a circular cylindrical tube having two walls that are transversely displaced by an infin...