Dr. Francesca Iacono

Dr. Francesca Iacono

Advisor / Co. Advisor

Prof. May / Prof. Dahmen

Dissertation

High-Order Adaptive Methods for Convection-Dominated Nonlinear Problems Using Multilevel Solution Techniques

Contact

Francesca Iacono
Email: iacono@aices.rwth-aachen.de

Education

12/2007 - 08/2011 Postgraduate Position at Aachen Institute for Advanced Study in Computational Engineering Science
(AICES), RWTH Aachen
11/2009 - 12/2009 Visiting student at the Department of Aerospace Engineering, Iowa State University, IA
04/2007 - 09/2007 Drawing up the M.Sc. thesis at the Institute for Numerical Mathematics, Universität Ulm, Germany
10/2005 - 10/2007 Master of Science in Mathematical Modelling in Engineering, Politecnico di Torino, Italy
09/2002 - 10/2005 Bachelor of Science in Mathematics for Engineering Sciences, Politecnico di Torino, Italy

Research interests


High-order adaptive methods for convection-dominated nonlinear problems using multilevel solution techniques

The spatial discretization of nonlinear hyperbolic PDE to high order of accuracy on unstructured meshes can be accomplished by local discretization methods, such as the Discontinuous Galerkin (DG) method, or the Spectral Difference (SD) Method. While a high order spatial discretization enables one to achieve better resolution with fewer degrees of freedom, the overall efficiency and robustness of a numerical scheme for large-scale applications depends on the solution methodology for the (nonlinear) system of equations arising from the discretization. Furthermore, efficiency and robustness can be defined in various ways, trading of such constraints as convergence properties, stability, CPU time, memory requirements, ease of implementation, and parallelizability.

For such nonlinear problems as high-Reynolds-number compressible fluid flow, efficiency and robustness of high order methods is still lagging behind best-practice (lower order accurate) industrial tools. To improve the status quo, one may identify convergence acceleration and adaptivity as two key technologies. Convergence acceleration, such as multigrid methods combined with efficient relaxation techniques, is paramount in increasing the efficiency of any solver, and rather mature for first and second order methods, most notably finite volume schemes. While established concepts usually allow an extension to higher order methods, the constraints often change dramatically (e.g. storage requirements). In practice, for most problems of practical interest, such as steady-state problems in transonic aerodynamics, no high-order solver currently achieves a faster turnaround compared to current state-of-the-art second order methods.

Compressible fluids flow often produce discontinuities, such as compression shocks, which make it necessary to design high-order schemes with shock capturing capabilities, which complicates the problem enormously. Adaptive mesh refinement enables the capture of very small scales of shock waves by lower order approximations without degrading the overall accuracy. Adaptation methods based on wavelets, induced by a multisresolution analysis, are very attractive. While these techniques have been successfully used with finite-volume solvers, the extension to higher order DG discretizations using so-called multiwavelets is yet to be fully developed. The potential, however is tremendous: the multiscale analysis framework, formulated on a tree of nested meshes, allows a unified treatment of mesh adaptation and multigrid solution methods within a solver architecture equipped with a compact, algorithmically optimal data structure. Limiter functions may also be defined based on the regularity properties of the solution esablished by the multiresolution analysis.

AICES funded research project

Publications

Dissertations


"The theory of variational inequalities and its application to an elastoplastic problem",
B.Sc. thesis, Politecnico di Torino, Italy, October 2005

“Reduced-basis methods for nonlinear convection-diffusion-reaction problems",
M.Sc. thesis, Politecnico di Torino, Italy, October 2007

“High-order methods for convection-dominated nonlinear problems using multilevel techniques",
Ph.D. thesis, RWTH Aachen, Germany, September 2011 (available online on RWTH library website)

Journal papers

A Hybrid Multilevel Method for High-Order Discretization of the Euler Equations on Unstructured Meshes,
G. May, F. Iacono and A. Jameson, J. Comput. Phys., Vol. 229, pp. 3938-3956, 2010

A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows,
F. Iacono, G. May, S. Mueller and R. Schaefer, submitted to J. Comput. Phys., 2011


Conference papers

Efficient Algorithms for High-Order Discretizations of the Euler and Navier-Stokes Equations,
G. May, F. Iacono and A. Jameson, 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, January 2009

Convergence Acceleration for Simulation of Steady-State Compressible Flows Using High-Order Schemes,
F. Iacono and G. May, AIAA paper number 2009-4132, 19th AIAA Computational Fluid Dynamics Conference, San Antonio, Texas, June 2009

Relaxation Techniques for High-Order Discretizations of Steady Compressible Inviscid Flows,
F. Iacono, G. May and Z.J. Wang, AIAA paper number 2010-4991, 40th AIAA Fluid Dynamics Conference, Chicago, Illinois, June 2010

An Adaptive Multiwavelet-based DG Discretization for Compressible Fluid Flow,
F. Iacono, G. May, S. Mueller and R. Schaefer, 6th International Conference on Computational Fluid Dynamics, St. Petersburg, Russia, July 2010

A Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows,
F. Iacono, G. May, S. Mueller and R. Schaefer, AIAA paper number 2011-0200, 49th AIAA Aerospace Sciences Meeting, Orlando, Florida, January 2011


Posters

“High-Order Methods for Convection-Dominated Nonlinear Problems",
AICES MIT Spring School 2009, RWTH, Aachen, Germany, March 2009

Presentations

“Convergence Acceleration for Simulation of Steady-State Compressible Flows Using High-Order Schemes",
19th AIAA Computational Fluid Dynamics Conference, San Antonio, Texas, June 24th, 2009

“High-Order Methods for Convection-Dominated Nonlinear Problems Using Multilevel Solution Techniques",
Department of Aerospace Engineering, Iowa State University, Ames, Iowa, November 18th, 2009

Nonlinear Preconditioning for High-Order Discretizations of Steady Compressible Inviscid Flows",
40th AIAA Fluid Dynamics Conference, Chicago, Illinois, June 30th, 2010

An Adaptive Multiwavelet-based DG Discretization for Compressible Fluid Flow",
6th International Conference on Computational Fluid Dynamics, St. Petersburg, Russia, July 16th, 2010

Who Really Invented Finite Elements, why Nobody Cared, and What Von Neumann had to do with it",
with M. Bachmayr, Students' talks on Friday, AICES, RWTH Aachen, November 26th, 2010

A Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows",
49th AIAA Aerospace Sciences Meeting, Orlando, Florida, January 4th, 2011

AC.CES 2011


See dedicated page

Students' talks on Friday

See dedicated page