·    Developing algorithms for parallel scientific computing.

My primary area of interest is developing highly scalable numerical algorithms and parallel software for simulations of various nontrivial hydrodynamic phenomena in fluid mechanics. I utilize an open source numerical package MUMPS (Multi Frontal Massively Parallel sparse direct Solver) to develop Full Pressure Coupled Direct (FPCD) time marching algorithm for time integration of incompressible Navier Stokes equations. Along with this I developed   my own PAR-ASA-CLGS code based on the iterative multigrid approach. The both solvers utilize the fully pressure-velocity coupled approach for incompressible flows. PAR-ASA-CLGS has been successfully tested on HLRN II massively parallel supercomputer in solving Navier-Stokes equations with over 32 Million degrees of freedom on 2048 cores. The algorithm achieved N/log(N) and N/ln(N) in a strong scalability test for single- and multigrid configurations respectively reaching the theoretical asymptotic limit.

 

The developed multigrid algorithm has been successfully applied to a stability analysis of the flow inside three dimensional lid-driven and differentially heated cavities, determining the main characteristics of the instability onset mechanism when going from steady to periodic flow.

Lid Driven Cavity

Differentially  Heated Cavity

 

lid                                                                                         

 

 

convect

 

 

 

 

 

 

 

 

 

 

 

 

 

·    Numerical Benchmarking

We propose a new benchmark case of a fully three-dimensionally flow in a cubic cavity driven by the lid moving at 45º relatively to its lateral boundaries.  This flow has no any two-dimensional similarities, and the velocity components are equally large in x- and z- directions. The flow exhibits interesting and not yet studied three-dimensional flow patterns, as is shown in the figure below  for Re=103.

 

 

 

 

 

 

 

 

 

 


·    Adapting of the developed algorithms to the linear stability analysis.

Figure 3.1.  

Perturbation of  vx

 
The work has been performed in collaboration with Laurette Tuckerman (PMMH-ESPCI). We investigate a potential of utilizing of the developed time marching numerical algorithms for the linear stability analysis. The FPCD approach utilizing the LU decomposition of the Stokes operator, shows competitive computational times and was successfully applied to the linear stability analysis for two-dimensional problems. In the following picture we show a distribution of the absolute values of the most unstable eigenmode of the main flow characteristics , for two dimensional lid-driven cavity, obtained on  200 ª 200 grid for Re=8700

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


However the FPCD approach  remains restricted by available computer memory when is applied to three-dimensional models. Assuming that this restriction will be removed in near future this approach should not be immediately neglected.

·    Applied engineering analysis using commercial Fluent -Ansys Software

We performed a full scale CFD elliptic analysis of anisotropic flow in the wake of a wind turbine. Special techniques of grid refinement were developed in order to provide accurate pressure and velocity distributions in the vicinity of the turbine blades and to ensure overall convergence and stability of the nu merical solution.

 

 

 

 

 

 

 

 

 


The proposed model implementation requires no extra features other than those available in a commercial code, and may be a powerful instrument for wind turbine engineers.  The whole study report is located here.