R & D Activities

a. Scope and aims of the R&D activities

The scope and aims of the R&D activities of the Scientific Computing and numerical analysis group are summarized in the following table.

• Development and application of high-order accurate methods for computations of compressible and incompressible flows
  
  
  • Computation of flows including strong discontinuities, LES of compressible turbulence.
    (Ekaterinaris, Vavilis)
  • Direct computation of noise generated by high-speed flows.
    (Ekaterinaris)
  • Computation of compressible flow with strong magnetic effects used for flow control.
    (Toulopoulos, Ekaterinaris).
  • LES of incompressible flows using high order, energy preserving numerical schemes.
    (Kampanis, Ekaterinaris)
    
  
  
• Development of Biomedical computation approaches using specific patient data obtained from medical imaging and geometry reconstruction techniques

• Three-dimensional reconstruction and preparation of organ geometries (abdominal aorta, bone, vertebrates etc.) using level set methods and other computational techniques.
  (Papaharilaou, Manousaki)
• Evaluation of abdominal aorta aneurysms (AAA) rapture risk, generation and proliferation based on computed flowfield information.
  (Papaharilaou, Katsamouris, Ekaterinaris)

• Flow-structure interaction and evaluation of rapture risk for patient specific AAA's.
  (Papaharilaou, Katsamouris, Ekaterinaris)

• Development and application of fast and accurate methods for acoustic wave propagation
  • Rotor noise propagation and use of optimisation techniques for the reduction of noise level.
    (Flouri, Ekaterinaris, Kampanis)

• Numerical methods for parabolic approximations and the Helmholtz equation in complex underwater waveguides
  (Dougalis, Kampanis, Mitsoudis, Zouraris, Antonopoulou)

• Coastal hydrodynamics
  • Sustainable coastal management. Applications to the Northern Crete coast.
    (Kampanis, Koutantos, Flouri)

• Numerical modelling in hydrology
  • Numerical modelling of floods
    (Kampanis, Flouri)

• Ground water management: diffusion of pollutants and mixing process with salt water.
  Kampanis, Flouri)

• Nonlinear Dispersive Waves
  • Numerical methods for water wave model equations and numerical approximation of blow-up for the Nonlinear Schrodinger Equation.
    (Dougalis, Mitsotakis)

b. Main accomplishments 2000-2004

1. State-of-the-art developments on high-order accurate numerical methods for compressible flows, carried out by the group over the past few years, give us now the capability to actively participate in competitive European projects that include accurate computations of complex flows. (GOAHEAD is an example of these projects.) In addition, we are currently participating in three more proposals for the 6th Framework Program that also require high fidelity flow computations.
2. Expertise on parallel computing acquired by the group over the last few years make now large-scale scientific computations possible at IACM. The high-speed jet noise project is an example of this type of application.
3. The additional capability of computing high-order accurate compressible flow solutions in complex domains using the discontinuous Galerkin approach has been established.
4. Over the last few years, capabilities for biomedical blood flow simulations were developed. At this stage complex 3d flows with advanced mesh geometry and visualization capabilities are being simulated.
5. Recently Dr. I. Ekaterinaris was invited by Cambridge University Press to write a book on recent development of high order methods for aerodynamics. This book will be published soon. In addition, another book on novel methods for numerical wave propagation edited by Prof. V. Dougalis, Dr. N. Kampanis and Dr. I. Ekaterinaris will be published by CRC Press.
6. Through its cooperation with the INRIA water resources management group, the ERCIM Environmental Modelling Group and other partners, the group has installed and further developed a library of codes for environmental flows simulation, including coastal hydrodynamics and hydrology codes.
7. Important research on the numerical analysis of P.D.E.'s was carried out by members of the group. Highlights: Accurate numerical simulation of solitary waves of model equations of water wave theory. Numerical verification of the 'log log' blow-up rate for the critical Nonlinear Schr?dinger Equation. Numerical analysis of the Parabolic Equation in Underwater Acoustics in variable topography domains. Numerical Analysis of differential equations with stochastic terms. High order finite volume methods.
8. Members of the group organized seven international workshops and conferences in Crete. They also organized nine sessions in international conferences, gave short courses, and served as members of the organizing or scientific committees of several international meetings.
9. Two Ph.D. dissertations in Numerical Analysis (D. Antonopoulos, D. Mitsoudis) were completed with IACM support (Advisor: V. Dougalis). Four more Ph.D. dissertations are in progress with members of the group as advisors. Several Master's Theses and Diploma Theses were also supervised by group members.
   

c. Publications in refereed journals, 2000-2004.

1. Ekaterinaris, J. A. and Kampanis, N. A., "A numerical prediction of acoustic fields generated by wind turbines," Systems Analysis Modeling Simulation, v. 39, 2000, pp. 49-74.
2. Ekaterinaris, J. A., "Implicit High-Order in Space Algorithms for the Navier-Stokes Equations," AIAA Journal, v. 38, No. 9, Sept. 2000, pp. 1594-1602.
3. Weber, S., Jones, K. D., Ekaterinaris, J. A., and Platzer, M. F., "Transonic Flutter Computations for the NLR 7301 Supercritical Airfoil," Journal of Aerospace Science and Technology, v. 5, 2001, pp. 293-304.
4. Kampanis, N. A., and Ekaterinaris, J. A., "Numerical prediction of far-field wind turbine noise over terrain of moderate complexity," Systems Analysis Modeling Simulation, v. 41, 2001, pp. 107-122.
5. Ekaterinaris J. A., "Numerical Investigations of Dynamic Stall Active Control for Incompressible and Compressible Flows," Journal of Aircraft, v. 39, No. 1, Feb. 2002, pp. 71-78.
6. Castro, B. M., Ekaterinaris J. A., and Platzer, M. F., "Navier-Stokes Analysis of Wind-Tunnel Interference on Transonic Airfoil Flutter," AIAA Journal, v. 40, No. 7, 2002, pp. 1269-1276.
7. Ekaterinaris, J. A., "Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes," Journal of Computational Aeroacoustics, v. 2, No. 2, 2003, pp. 175-192.
8. Ekaterinaris, J. A., "Performance of High-Order Accurate Low-Diffusion Numerical Schemes for Compressible Flow," AIAA Journal, v. 42, No. 3, 2004, pp. 493-500.
9. Ekaterinaris, J. A., "Predictions of Performance with Active Flow Control on Airfoils and Wings," Journal of Aerospace Science and Technology, v. 8, 2004, pp. 401-410.
10. Ekaterinaris, J. A., "High-Order Accurate Numerical Solution of Incompressible Flows with the Artificial Compressibility Method," International Journal of Numerical Methods in Fluids. Vol. 45, 2004, pp. 1187-1207.
11. Flouri, E., Ekaterinaris, J. A., and Kampanis, N. A., "High-Order Accurate Solutions for the Parabolic Equation," Accepted for publication (May 2004) in the Journal of Computational Acoustics.
12. N. A. Kampanis, "Numerical simulation of low-frequency aeroacoustics over irregular terrain using a finite element discretization of the parabolic equation," J. Comp. Acoustics, v. 10, No 1, (2002), 97-112.
13. N. A. Kampanis, E. T. Flouri, "A GIS interfaced numerical model for the simulation of sound propagation in the atmosphere over irregular terrain," Systems Analysis Modelling Simulation, v. 43, No 9, (2003), 1199-1212.
14. Dougalis V. A., Pelloni B., "Numerical solution of some nonlocal, nonlinear, dispersive wave equations," J. Nonlin. Science, v. 10, 2000, pp. 1-22.
15. Dougalis V. A., Pelloni B., "Numerical modelling of two-way propagation of nonlinear dispersive waves," J. Math. and Computers in Simulation, v. 55, 2001, pp. 595-606.
16. Dougalis V. A., Pelloni B., "Error estimates for a fully discrete spectral scheme for a class of nonlinear nonlocal dispersive waves," Appl. Numer. Math., v. 37, 2001, pp. 95-107.
17. Akrivis, G. D., Dougalis, V. A., and Zouraris, G. E., "Finite difference schemes for the 'parabolic' equation in a variable depth environment with a rigid bottom boundary condition," SIAM J. Numer. Anal., v. 39, 2001, pp. 539-565.
18. Akrivis, G. D., Dougalis, V. A., Karakashian, O. A., and McKinney W. R., "Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schr?dinger equation," SIAM J. of Scientific Computing, v. 25, 2003, pp. 186-212.
19. Vardoulakis, I., Vairaktaris, E., Papamichos, E. and Dougalis, V. A., "Subsidence diffusion-convection, II : Inverse Problem," Computer Methods in Appl. Mech. and Engrg., v. 193 (27-29), 2004, pp. 2761-2770.
20. Zouraris, G. E., "On the convergence of a linear conservative two-step finite element method for the nonlinear Schr?dinger equation," Math. Model. Numer. Anal., v. 35, 2001, pp. 389-405.
21. Zouraris, G. E., Szepessy, A. and Tempone A., "Adaptive weak approximations of stochastic differential equations," Comm. in Pure and Appl. Mathematics, v. 54, 2001, pp. 1169-1214.
22. Moon, K.-S., Szepessy, A. Tempone, R., and Zouraris, G. E., "A variational principle for adaptive approximations of ordinary differential equations," Numer. Math., v. 96, 2003, pp. 131-152.
23. Moon, K.-S., Szepessy, A. Tempone, R., and Zouraris, G. E., "Convergence rates for adaptive approximation of ordinary differential equations," Numer. Math., v. 96, 2003, pp. 99-129.
24. Babuska, I., Tempone, R., Zouraris, G. E., "Galerkin finite element approximations of stochastic elliptic partial differential equations," SIAM J. Numer. Anal., v. 42, 2004, pp. 800-825.
25. Plexousakis, M. and Zouraris, G. E., "On the construction and analysis of high order locally conservative finite volume-type methods for one dimensional elliptic problems," SIAM J. Numer. Anal., v. 42, 2004, pp. 1226-1260.