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High Performance Computing
In Computational Fluid Dynamics and Aeroacoustics

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KSFD algorithm for Poisson equation with one periodic direction

Authors: A. Gorobets, F. X. Trias, M. Soria

The Krylov-Schur-Fourier Decomposition algorithm (KSFD): Fourier decomposition uncouples 3D problem into set of 2D problems (planes). The Preconditioned Conjugate Gradient (PCG) Krylov subspace iterative method and the Direct Schur Decomposition (DSD) direct method are used to solve the 2D problems

The KSFD solver is designed for large-scale DNS and LES on supercomputers.
  • It provides good performance and scalability, can work with large meshes using >10000 CPU
  • It performs well on both small "Beowulf" clusters and supercomputers
  • The problem to solve must have (at least) one periodic direction, mesh step must be uniform in this direction
  • The geometry of 3D obstacles is limited to be a 2D shape extruded along the periodic direction
  • More...


Parallel fully-3D Poisson solver

Authors: A. Gorobets, F. X. Trias, M. Soria

Multigrid approach is used to extend the KSFD solver to fully 3D cases. A "2.5D" approximation compatible with KSFD solver is used as a second level. A simple PCG with a local preconditioner is used as a smoother.

The extended solver is designed for large-scale DNS and LES of fully 3D cases (3 wall-orthogonal directions, 3D obstacles, non uniform mesh in all 3 directions) on supercomputers.
  • It provides reasonable scalability, can work with moderate meshes (10~50*106) using >1000 CPU
  • But it has some limitations on mesh concentration
  • It is still under construction...
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