High Performance Computing
In Computational Fluid Dynamics and Aeroacoustics

Personal page of A. Gorobets


The parallel in-house research CFD CAA code NOISETTE


Computational Aeroacoustics Laboratory

Institute for Mathematical Modelling (IMM) of Russian Academy of Science (RAS)


   INRIA Sophia Antipolis, France

  • Explicit high-order algorithms for unstructured 2D (triangular) and 3D (tetrahedral) meshes
  • DNS of compressible viscous flows and aeroacoustics (DNC, NLDE)
  • High efficiency on thousands of CPUs of a supercomputer even for small meshes
  • Hybrid MPI+OpenMP parallelization
  • Language: computational part - Fortran 90, infrastructure - C++
Authors: I. Abalakin, A. Gorobets, T. Kozubskaya, D. Kolmogorov, A. Duben, I. Borovskaya

Original sequential 2D version designed in IMM RAS together with INRIA, Sophia-Antipolis, France (Abalakin I. V., Kozubskaya T. K., A. Dervieux, C. Debiez)

Mathematical basis

  • Euler Equations (EE)
  • Navier-Stokes Equations (NSE)
  • Nonlinear Disturbances Equations (NLDE)
  • Linearized Euler Equations (LEE)
  • Linearized Navier-Stokes Equations (NSE)

Numerical Techniques Implemented

Space Approximation
      Multi-parameter vertex-centered scheme (up to 6th order)
Time Integration
      Runge-Kutta method, Low-storage Runge-Kutta method (up to 4th order)
      Linear Low-storage Runge-Kutta method (arbitrarily high order)
Boundary Conditions
      Steger-Warming flux splitting based inflow and outflow BC
      Characteristic BC
      Non-reflecting (radiation and outflow, buffer zones)
      Non-local transparent BC

Parallel performance

Parallel algorithm is based on a hybrid MPI+OpenMP approach which better fits modern architecture of a supercomputer with multi-core nodes. Following figures demonstrate high parallel efficiency even for a small problem. The high order scheme with the large space stencil is used in the tests.

Supercomputer MVS 100000 (JSC RAS)
Mesh size is only ~106 nodes

Supercomputer Lomonosov (MSU)
Mesh size 1.6*107 nodes

Current applications

  • Numerical experiments on acoustic liners (Jet engine noise reduction devices)
  • Optimization of acoustic sensors for mobile robots
  • Modeling of impedance tubes with resonator chambers
  • Complex flows around obstacles considering acoustic effects

Development directions

  • General object-oriented restructuring of the code (Gorobets, Kozubskaya)
  • Implementation of turbulence models RANS, DES, LES (Abalakin, Kolmogorov)
  • Implicit time integration algorithm (Abalakin, Kolmogorov)
  • Parallel algorithm improvements (Gorobets)
  • New types of boundary conditions - periodic BC, non-local BC, etc.
  • Infrastructure extension
  • A.V.Gorobets, T.K.Kozubskaya, “Technology of parallelization of the explicit high-accuracy algorithms for CFD and CAA on non-structured meshes”, Mathematical modeling, vol. 19, number 2, pp. 68-86, 2007
  • A.V. Gorobets, I.V. Abalakin, T.K. Kozubskaya, “Technology of parallelization for 2D and 3D CFD/CAA codes based on high-accuracy explicit methods on unstructured meshes”, Parallel CFD 2007, Antalya (Turkey), May 2007
  • Abalakin I.V., Dervieux A., Kozubskaya T.K. "High Accuracy Finite Volume Method for Solving Nonlinear Aeroacoustics Problems on Unstructured Meshes", Chinese Journal of Aeronautics, Vol. 19, No 2, 2006.
  • Tatiana K. Kozubskaya, "Validation and Verification in Computational Aeroacoustics: from Linear to Nonlinear" - In A series of Handbooks on Theory and Engineering Applications of Computational Methods. Verification and Validation Methods for Challenging Multiphysics Problems, CIMNE, Barcelona (2006), pp. 187-208
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