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12/07/2009
12/05/2009
Research Interests
Numerical solution of PDE’s. Computational fluid dynamics: finite element schemes for hyperbolic problems, design of new finite element schemes for hyperbolic conservation laws with time dependent boundary conditions, strong wave interactions, shocks, complex viscous flow features, flows in the presence of magnetic fields.
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Graphs DG, Aeroacoustic Problems
Radiation Boundary Conditions, Characteristic Boundary Conditions
Time harmonic source problem - Scattering by cylinder surface.
The computed pressure field using P3 local space and characteristic boundary conditions at the far field boundary part, see mypaper[3j].
Acoustic pulse scattering by a cylinder surface.
The computed pressure field using P3 local polynomial space and
characteristic boundary conditions at the boundaries, see my paper [3j].
Time harmonic source problem. Left: the pressure computed field using P3 local space using characteristic boundary conditions, Right: the variation of the L2 error measured on the boundary elements at every time step.
Propagation and reflection from a solid wall of an acoustic pulse.
The compute pressure field using radiation boundary conditions at the far field boundary parts. 
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12/04/2009
Graphs DG, Nonlinear Euler, Problems with Smooth Solutions
Steady state solutions, flow past over a cylinder
Flow past over a cylinder, the Mach number computed field using P5 local polynomial space. The cylinder surface is descritized using 90 elelements.
Flow past over a cylinder, the Mach number computed field using P5 local polynomial space. The cylinder surface is descritized using 90 elelements.
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Grpahs DG, Compressible Navier Stokes
Flow past over a cylinder
DG numerical solution of the viscous flow problem (flow past over a cylinder) using characteristic boundary conditions at the outflow boundary part of the computational domain, (toulio 2009, see mypaper 3j)
DG numerical solution of the viscous flow problem (flow past over a cylinder) using characteristic boundary conditions at the outflow boundary part of the computational domain, (toulio 2009, see mypaper 3j)
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Graphs DG, Nonlinear Euler Equations Discontinuous Solutions
Double Forward Facing Step, Double Mach Reflection
A new shock capturing scheme, using extrema control conditions (toulio 2009, see mypaper 8c)
A new shock capturing scheme, using extrema control conditions (toulio 2009, see mypaper 8c)
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3D Graphs DG, Nonlinear Euler equations
Steady state solutions, flow past over a cylinder
Steady state flow problems, flow past over a cylinder.
The subdivision of the 3 Dimensional computational domain by tetrahedral elements. The surface of the cylinder has been discretised using 20 elements
The Mach number computed field using P1 local polynomial space. Simple extrapolated inflow – outflow boundary conditions have been implemented.
Steady state flow problems, flow past over a cylinder.
The subdivision of the 3 Dimensional computational domain by tetrahedral elements. The surface of the cylinder has been discretised using 20 elements
The Mach number computed field using P1 local polynomial space. Simple extrapolated inflow – outflow boundary conditions have been implemented.
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Graphs of Numerical Solutions of Benchmark problems
- Graphs DG, Nonlinear Euler, Problems with Smooth Solutions
Steady state solutions, flow past over a cylinder - Graphs DG, Compressible Navier Stokes
Flow past over a cylinder - Graphs DG, Nonlinear Euler Equations Discontinuous Solutions
Double Forward Facing Step, Double Mach Reflection - Graphs DG, Aeroacoustic Problems
Radiation Boundary Conditions, Characteristic Boundary Conditions
- Graphs DG, Nonlinear Euler, Problems with Smooth Solutions
Steady state solutions, flow past over a cylinder
Flow past over a cylinder, the Mach number computed field using P5 local polynomial space. The cylinder surface is descritized using 90 elelements. - Graphs DG, Compressible Navier Stokes
Flow past over a cylinder
DG numerical solution of the viscous flow problem (flow past over a cylinder) using characteristic boundary conditions at the outflow boundary part of the computational domain, (toulio 2009, see mypaper 3j) - Graphs DG, Nonlinear Euler Equations Discontinuous Solutions
Double Forward Facing Step, Double Mach Reflection
A new shock capturing scheme, using extrema control conditions (toulio 2009, see mypaper 8c) 
- Graphs DG, Aeroacoustic Problems
Radiation Boundary Conditions, Characteristic Boundary Conditions
Time harmonic source problem - Scattering by cylinder surface.
The computed pressure field using P3 local space and characteristic boundary conditions at the far field boundary part, see mypaper[3j].
Acoustic pulse scattering by a cylinder surface.
The computed pressure field using P3 local polynomial space and
characteristic boundary conditions at the boundaries, see my paper [3j].
Time harmonic source problem. Left: the pressure computed field using P3 local space using characteristic boundary conditions, Right: the variation of the L2 error measured on the boundary elements at every time step.
Propagation and reflection from a solid wall of an acoustic pulse.
The compute pressure field using radiation boundary conditions at the far field boundary parts.
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12/03/2009
My Papers
Papers in journals
1j. I. Toulopoulos and J. A. Ekaterinaris ‘High-Order Discontinuous Galerkin Discretizations for Computational Aeroacoustics in Complex Domains’, AIAA Journal, Vol. 44, No. 3, 2006, pp. 502-511.
1j. I. Toulopoulos and J. A. Ekaterinaris ‘High-Order Discontinuous Galerkin Discretizations for Computational Aeroacoustics in Complex Domains’, AIAA Journal, Vol. 44, No. 3, 2006, pp. 502-511.
2j. G. Arabatzis, P. Vavilis, I. Toulopoulos and J. A. Ekaterinaris, ‘Implicit High-Order Time-Marching Schemes for the Linearized Euler Equations’ AIAA Journal, Vol. 45, No. 8,
2007, pp 1819-1826.
3j. I. Toulopoulos and J. A. Ekaterinaris ‘Artificial boundary conditions for the numerical
solution of the Euler equations by the discontinuous Galerkin finite element method’
submitted to a journal.
4j I. Toulopoulos and C. Makridakis "A new discontinuous Galerkin scheme for the numerical solution of flow problems with discontinuities"
submitted for publishing
Papers in conferences
3c. I. Toulopoulos and J. A. Ekaterinaris ‘Discontinuous Galerkin Discretizations for Viscous Flow Problems in Complex Domains’, 43th AIAA Aerospace Science Meeting and Exhibit, 10-13 Jan. 2005, Reno-Nevada, USA AIAA paper 1265.
4c. I. Toulopoulos and J. A. Ekaterinaris ‘High resolution Compressible flow Simulations with the discontinuous Galerkin Method’, 17th AIAA Computational Fluid Dynamics Conference, 6-9 June 2005, Toronto Canada, AIAA paper 5109.
5c. I. Toulopoulos and J. A. Ekaterinaris ‘Implementation of Characteristic boundary conditions to the discontinuous Galerkin Method’, 44th AIAA Aerospace Science Meeting and Exhibit, 9-12 Jan. 2006, Reno-Nevada, USA AIAA paper 0108.
6c. I. Toulopoulos and J. A. Ekaterinaris ‘High order shock capturing discontinuous Galerkin schemes’ Proceedings of European Conference on Computational Fluid Dynamics, 5-8 September 2006, Egmond aan Zee, Holland, editors P. wasseling, E. Onate, J. Periaux.
7c. I. Toulopoulos and J. A. Ekaterinaris ‘On the Application of Filters for Discontinuity Capturing with High Order Discontinuous Galerkin Discritizations’ International Workshop on High-order Finite Element Methods, 17-19 May 2007, Herrsching am Ammersee (near Munich), Germany.
8c. I. Toulopoulos and C. Makridakis ‘A discontinuous Galerkin shock-capturing scheme for the numerical solution of compressible flow problems’, Proceeding of Conference in Numerical Analysis (NumAn 2008), pages 195-200, 1-5 September 2008, Kalamata Greece, editors G. Akrivis,E. Gallopoulos, A. Hadjidimos, I. S. Kotsireas, D. Noutsos, M. N. Vrahatis.
Other reserch contributions for conservation laws.
DG Implicit schemes for nonlinear Euler equations
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