Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Sviluppo e validazione di un modello di film fluido per simulazioni CFD di motori a combustione interna

A wall film model has been implemented in a customized version of KIVA code developed at University of Bologna. Under the hypothesis of `thin laminar ow' the model simulates the dynamics of a liquid wall film generated by impinging sprays. Particular care has been taken in numerical implementation of the model. The major phenomena taken into account in the present model are: wall film formation by impinging spray; body forces, such as gravity or acceleration of the wall; shear stress at the interface with the gas and no slip condition on the wall; momentum contribution and dynamic pressure generated by the tangential and normal component of the impinging drops; film evaporation by heat exchange with wall and surrounding gas. The model doesn't consider the effect of the wavy film motion and suppose that all the impinging droplets adhere to the film. The governing equations have been integrated in space by using a finite volume approach with a first order upwind differencing scheme and they have been integrated in time with a fully explicit method. The model is validated using two different test cases reproducing PFI gasoline and DI Diesel engine wall film conditions.