MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1249 products
-
34/2010 - 11/09/2010
Abba', A.; Bonaventura, L.
A mimetic finite difference method for Large Eddy Simulation of incompressible flow | Abstract | | A finite difference discretization of the three-dimensional, incompressible Navier-Stokes equations is presented, based on finite difference operators that satisfy discrete analogs of some basic calculus identities. These
mimetic properties yield a numerical method for which a discrete form of the vorticity equation can be derived naturally from the discrete momentum equation, by application of the mimetic rotation operator. As a result,a discrete approximation of vorticity is exactly preserved, for inviscid flows, independently of the mesh size. The vorticity preservation property guarantees that no spurious vorticity is generated by the nonlinear advective terms in absence of viscosity. A mimetic discretization of the viscous terms and an appropriate treatment for rigid wall boundary conditions are also
proposed. The relationship of this approach to other similar techniques is discussed. The proposed method is validated on several idealized test cases for laminar incompressible flow, in which it is compared to a widely used finite difference discretization. The method is then applied to Large Eddy Simulation of incompressible flow, demonstrating the advantages of the inherentconservation properties in a comparison with experimental data and DNS results especially when strong vorticity production takes place at the boundaries. |
-
33/2010 - 11/08/2010
Migliorati, Giovanni; Quarteroni, Alfio
Multilevel Schwarz Methods for Elliptic Partial Differential Equations | Abstract | | We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic Partial Di fferential Equations by the fiite element method. In our
analysis we deal with unstructured mesh partitions and with subdomain boundaries resulting from using the mesh partitioner. We start from two-level preconditioners with either aggregative or interpolative coarse level
components, then we focus on a strategy to increase the number of levels. For all preconditioners, we consider the additive residual update and its multiplicative variants within and between levels. Moreover, we compare the preconditioners behaviour, regarding scalability and rate of convergence. Numerical results are provided for elliptic boundary-value problems, including a convection-di ffusion problem when suitable stabilization
becomes necessary. |
-
32/2010 - 11/07/2010
Malossi, A. Cristiano I.; Blanco, Pablo J.; Deparis, Simome; Quarteroni, Alfio
Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows | Abstract | | The main goal of the present work is to devise robust iterative strategies to partition the solution of the Navier–Stokes equations in a three-dimensional(3D) computational domain, into non overlapping 3D subdomains,which communicate through the exchange of integrated quantities
across the interfaces. The novel aspect of the present approach is that at coupling boundaries the conservation of flow rates and of the associated dual variables is imposed, entailing a weak physical coupling. For the solution
of the non-linear problem, written in terms of interfaces variables, two strategies are compared: relaxed fixed point iterations and Newton iterations. The algorithm is tested in several configurations for problems which involve more than two components at each coupling interface. In such cases it is shown that relaxed fixed point methods are not convergent, whereas the Newton method leads in all the tested cases to convergent schemes. One of the appealing aspects of the strategy proposed here is the
flexibility in the setting of boundary conditions at branching points, where no hierarchy is established a priori, unlike classical Gauss–Seidel methods.
Such an approach can be applied in two other different contexts: (i) when coupling dimensionally-heterogeneous models, just by replacing some of the 3D models by one-dimensional (or zero-dimensional) condensed ones, and (ii) as a preconditioner method for domain decomposition methods for the
Navier–Stokes equations. These two issues are also addressed in the present work. Finally, several examples of application are presented, ranging from academic examples to some related to the computational hemodynamics field. |
-
31/2010 - 11/06/2010
Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi
Shape optimization for viscous flows by reduced basis methods and free-form deformation | Abstract | | In this paper we present a new approach for shape optimization that combines two different types of model reduction: a suitable low-dimensional
parametrization of the geometry (yielding a geometrical reduction) combined with reduced basis methods (yielding a reduction of computational complexity). More precisely, free-form deformation techniques are introduced
for the geometry description and its parametrization, while reduced basis methods are used upon a finite element discretization to solve systems of parametrized partial differential equations. This allows an efficient flow field computation and cost functional evaluation during the iterative optimization
procedure, resulting in effective computational savings with respect to usual shape optimization strategies. This approach is very general
and can be applied for a broad variety of problems. To prove its effectivity, in this paper we apply it to find the optimal shape of aorto-coronaric bypass anastomoses based on vorticity minimization in the down-field region.
Stokes equations are used to model blood flow in the coronary arteries. |
-
30/2010 - 11/05/2010
Blanco, Pablo J.; Discacciati, Marco; Quarteroni, Alfio
Modeling dimensionally-heterogeneous problems: analysis, approximation and applications | Abstract | | In the present work a general theoretical framework for coupled dimensionally-heterogeneous partial differential equations is developed. This isdone by recasting the variational formulation in terms of coupling interface variables. In such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation. This approach also allows the development of different iterative substructuring solution methodologies involving dimensionallyhomogeneous
subproblems. Numerical experiments are carried out to test our theoretical results.
Keywords: Multiphysics, Heterogeneous PDE models, Augmented formulation,Domain decomposition, Finite elements. |
-
29/2010 - 11/04/2010
Lesinigo, Matteo; D'Angelo, Carlo; Quarteroni, Alfio
A multiscale Darcy-Brinkman model for fluid flow in fractured porous media | Abstract | | The aim of this work is to present a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures.
The Darcy s law is assumed in the porous domain while the Stokes-Brinkman equations are considered in the fractures. We address the case of fractures whose thickness is very small compared to the characteristic diameter of the
computational domain, and describe the fracture as if it were an interface between porous regions. We derive the corresponding interface model governing the fluid flow in the fracture and in the porous media, and establish the
well-posedness of the coupled problem. Further, we introduce a finite element scheme for the approximation of the coupled problem, and discuss solution strategies. We conclude by showing the numerical results related to several test cases and compare the accuracy of the reduced model compared with the non-reduced one. |
-
28/2010 - 11/03/2010
Crosetto, Paolo; Reymond, Philippe; Deparis, Simone; Kontaxakis, Dimitrios; Stergiopulos, Nikolaos; Quarteroni, Alfio
Fluid Structure Interaction Simulations of Physiological Blood Flow in the Aorta | Abstract | | The numerical tools to simulate blood flow in the cardiovascular system are constantly developing due to the great clinical interest and to scientifi c advances in mathematical models and computational power. The present work aims to address and validate new algorithms to efficiently predict the hemodynamics in large arteries. The latter rely on fi nite elements simulation of the fluid-structure interaction between blood flow and arterial wall deformation of a healthy aorta. Di fferent sets of boundary conditions are devised and tested. The mean velocity and pressure time evolution is plotted
on di erent sections of the aorta and the wall shear stress distribution is computed. The results are compared with those obtained with a rigid wall simulation. Pulse wave velocity is computed and compared with the values available from the literature. The flow boundary conditions used for the outlets are obtained using the solution of as one dimensional model. The results of the simulations are in agreement with the physiological data in terms of wall shear stress, wall displacement, pressure waveforms and velocities. |
-
27/2010 - 11/02/2010
Bruggi, Matteo; Verani, Marco
An adaptive algorithm for topology optimization with goal-oriented error control | Abstract | | We present an adaptive scheme, named ATOPT algorithm, to address volume–constrained compliance minimization, a benchmark problem in topology optimization.
The algorithm performs a set of optimization loops on an underlying grid that is iteratively adapted to improve the description quality of the topology of the structure and the accuracy of the finite element compliance approximation of the
evolving solution. Two suitable error estimators are defined in order to address both the issues. Numerical simulations show that ATOPT algorithm achieves optimal layouts that are in full agreement with standard results obtained by employing large scale uniformly refined grids. However, the ATOPT algorithm turns out to be more
accurate in terms of the approximation of both the elastic behavior and the topology, while the computational cost spent in the minimization algorithm is remarkably reduced.
Keywords: topology optimization, minimum compliance, adaptive mesh refinement.
2000 Mathematics Subject Classification. 65N30, 93B40 |
|
