in this work a numerical study of thermal and fluid dynamics behavior of natural air convection in a square cavity in a laminar flow is presented, by finite volume method. the square cavity has two walls heated with different temperatures and two isolated walls. the numerical simulation is made up of several rayleigh numbers to . flow and isotherm lines are presented and analyzed. the numerical...

We will overview a series of recent works [1, 2, 3, 4, 5, 6, 7] all related to some multiscale problems motivated by practical problems in Mechanics. The common denominator of all these works is that they address multiscale problems where the geometry of the microstructures is not periodic. Random modelling, but not only (see e.g. [2, 3]), can then be used in order to account for the imperfecti...

In the 1 International Workshop, devoted to Trefftz Method, the author presented an indirect approach to Trefftz Method (Trefftz-Herrera Method), while in the Second one some of the basic ideas of how to integrate different approaches to Trefftz method were introduced. The present Plenary Lecture, corresponding to the 3 International Workshop of this series, is devoted to show that Trefftz Meth...

In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. We provide a convergence analysis of the numerical method, derived based upon properties of the equation being solved and without the need to impose smoothness conditions on the solution. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method...

the main purpose of this article is to increase the efficiency of the least squares method in numerical solution of ill-posed functional and physical equations. determining the least squares of a given function in an arbitrary set is often an ill-posed problem. in this article, by defining artificial constraint and using lagrange multipliers method, the attempt is to turn -dimensional least squ...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...