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Development of Vortex Methods for Grid-free Lagrangian Simulations of Reacting Flows in 2D and 3D Bounded Domain

Vortex Methods for 3D Flows

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Key issues include:

  • Enforcing the divergence-free condition on the vorticity field

  • Accurate and efficient handling of the vorticity stretching/tilting term

  • diffusion near boundaries

  • no-slip boundary conditions

  • spatial adaptivity

  • baroclinic vorticity generation

  • volumetric expansion

  • reaction source terms in the energy and species equations.

Diffusion is simulated using the Smoothed Redistribution Method

Collision of Two Vortex Rings. Reynolds Number = 10000. Number of elements increased from 2744104 to 6509964.

Vortex Methods for 2D Flows

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Key issues include:

  • diffusion near boundaries of complex geomtries

  • no-slip boundary conditions

  • spatial adaptivity

  • baroclinic vorticity generation

  • volumetric expansion

  • reaction source terms in the energy and species equations.

spatial adaptivity enables resolving the wake just behind the cylinder with more elements than far from the cylinder.

Diffusion near bounderies of complex geometries

Natural convection of a hot patch.

High Reynolds Number (Re=9500) flow over a cylinder

Wake behind a cylinder undergoing harmonic angular oscillations

Simulation of a Jet Fluidic Oscillator

  • Lakkis, Issam: Grid-Free Vortex Methods for Natural Convection; Handling Source Terms and Nonlinear Diffusion. In: Numerical Heat Transfer, Part B: Fundamentals 62 (2012), Nr. 5, S. 370–398

  • Lakkis, Issam ; Ghoniem, Ahmed: A high resolution spatially adaptive vortex method for separating flows. Part I: Two-dimensional domains. In: Journal of Computational Physics 228 (2009), Nr. 2, S. 491–515

  • Lakkis, Issam ; Ghoniem, Ahmed F.: Axisymmetric vortex method for low-Mach number, diffusion-controlled combustion. In: Journal of Computational Physics 184 (2003), Nr. 2, S. 435–475

  • Lakkis, Issam A. ; Ghoniem, Ahmed F.: Grid-free simulation of a reacting radiating fuel ring. In: AIAA, Aerospace Sciences Meeting and Exhibit, 38 th, Reno, NV (2000)

  • Lakkis, I ; Ghoniem, Ahmed F.: Grid-free simulation of radiative transport in a participating medium. In: ESAIM: Proceedings 7 (1999), S. 234–246

  • Lakkis, Issam ; Ghoniem, Ahmed F.: Lagrangian simulation of fire plumes. In: ASME-PUBLICATIONS-HTD 357 (1998), S. 215–226

  • Ghoniem, Ahmed F. ; Lakkis, Issam ; Soteriou, Marios: Numerical simulation of the dynamics of large fire plumes and the phenomenon of puffing. In: Symposium (International) on Combustion 26 (1996), Nr. 1, S. 1531–1539

  • Lakkis, Issam: GRID-FREE VORTEX METHODS FOR NATURAL CONVECTION IN TWO-DIMENSIONAL DOMAINS. In: Proceedings of ASME 2012 International Mechanical Engineering Congress and Exposition 2012, 2012

  • Lakkis, Issam: A mesh-free redistribution method for the simulation of diffusion in arbitrary domains. In: Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics MIT, 2009

  • Ghoniem, A.F. ; Lakkis, I.A.: Towards Lagrangian, grid free simulation of combustion. In: Proceedings of the first MIT Conference on Computational Fluid and Solid Mechanics. Cambridge, MA, 2001, S. 1188–1191.

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