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Dmitry Gokhman
Research
- Hybrid systems: coming soon ...
- Applications of the continuous wavelet transform to partial differential equations: coming soon ...
- Scientific computation with Numerical Python: Numerical Python (Numpy) is an extension of the Python language by Guido Weiss. Numpy combines the flexibility, readability, and abstraction of an interpreted object oriented language with the speed of precompiled linear algebra routines. Current work deals with implementation of various classes arising in scientific computing (e.g. cubic and quintic parametric splines).
- Computational Fluid Dynamics for incompressible internal flow:
This work with A. Gokhman is motivated by problems arising in analysis and design of hydroturbines. The main goal is to develop and implement fast, highly accurate algorithms for computing water flow through hydroturbine passages.
- Potential flow: The potential flow turbine (PQT) invented by A. Gokhman achieves flow that is nearly potential. The main tool for computing potential flow is the boundary element method (BEM).
BEM suffers from the drawback of intricate setup and having to solve linear systems with hightly populated matrices, but offers the tremendous advantage of needing to discretize only the boundary, which has codimension 1.
The axisymmetric irrotational component of the flow can be modeled by distributions of circular vortex filaments on the bounding surfaces of the passage. Since the problem has cylindrical symmetry, it is essentially 2-dimensional.
Current work centers on the 3-dimensional problem of the remaining component of flow satisfies zero boundary conditions all around. The hydroturbine blades are modeled by a vortex filaments through the axis, through the blades and out of the passage, combined with source/sink distributions on the bounding surfaces of the passage and on the surfaces of the blades.
- Viscous/turbulent flow: Here BEM is not applicable and the finite element method (FEM, a.k.a. Bubnov-Galerkin method) runs into serious difficulties at the boundary for flows with high Reynolds numbers (around 107). The main difficulty lies in the fact that most common shape functions are inadequate in describing the tremendous increase of velocity from zero at the wall to almost mean velocity through the passage a short distance from the wall. An iterated modification of FEM by parametric splining by A. Gokhman dealt with these difficulties in the case developed flow through a cylindrical pipe. Current work centers on extending this technique to undevelped flow and to more general passage geometry.
- Potential flow: The potential flow turbine (PQT) invented by A. Gokhman achieves flow that is nearly potential. The main tool for computing potential flow is the boundary element method (BEM).
BEM suffers from the drawback of intricate setup and having to solve linear systems with hightly populated matrices, but offers the tremendous advantage of needing to discretize only the boundary, which has codimension 1.
Last updated: Jun 17 18:52 / Last fetched: Thu Jul 3 20:10:39 CDT 2008