Sharif Digital Repository

In this study, fluid-solid interaction (FSI) is simulated computationally by using a high-order accurate numerical method. The two-dimensional incompressible viscous flows are considered in the fluid domain. The primary problem with solutions of the incompressible Navier–Stokes equations is the difficulty of coupling changes in the velocity field with changes in the pressure field while satisfying the continuity equation. Herein, the artificial compressibility method is used to overcome this difficulty. Preconditioning is implemented to reduce the stiffness of the system of equations to increase the convergence rate of the solution. Using preconditioning, physical solutions even at low... 

In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. Later, Raydan derived an interesting relationship between a gradient method and the shifted power method. This relationship allows one to establish the convergence of the Barzilai and Borwein method when applied to the problem of minimizing any strictly convex quadratic function. With this point of view, he explained the remarkable improvement obtained by using this new choice of steplength. For some special cases, he presented some very interesting convergence rate results.... 

The main goal of this work is solving system of linear equations Ax = b, where A is a n_n square matrix, b is a n_1 vector and x is the vector of unknowns. When n is large, using direct methods is not economical. Thus, the system is solved by iterative methods. At first, projection method onto subspace K _ Rn with dimension m _ n is described, and then this subspace K is equalized with the krylov subspace. Then,some samples of projection methods onto the krylov subspace, such as FOM, GMRES and CG (Conjugate Gradient), are considered. The preconditioning of the linear system is explained, that is, instead of solving system Ax = b, the system PAx = Pb (P nonsingular), is solved, such that the... 

In the present study, the numerical simulation of the compressible inviscid flow around helicopter rotor is performed using the solution of the preconditioned Euler equations. Three preconditioners proposed by Eriksson, Choi and Merkel, and Turkel are implemented in two- and three-dimensional upwind Euler flow solvers on unstructured meshes. The mathematical formulations of these preconditioning schemes for different sets of primitive variables are drawn and their eigenvalues and eigenvectors are compared with each others. For this aim, these preconditioning schemes are expressed in a unified formulation. A cell-centered finite volume Roe's upwind method is used for the discretization of the... 

In this study, an accurate numerical solution of the two-dimensional incompressible viscous flows is performed by using the spectral difference method on structured grids. The system of equations to be solved here is the preconditioned incompressible Navier-Stokes equations in the primitive variable formulation with the artificial compressibility approach. In the spectral difference method, two sets of the structured points, namely, “solution points” and “flux points” are defined in each cell for supporting the reconstruction of desirable order of accuracy. Here, the formulation of the spectral difference method is derived and the representative form of the solution and flux points for...