S. Tsynkov's Research Areas
(to be updated)
Artificial Boundary Conditions (ABCs) for External Aerodynamics.
ABCs are generally needed for solving infinite-domain problems on the computer
as they allow to truncate the original unbounded domain and thus facilitate
creation of the finite-dimensional discretizations. Specific aerodynamic
applications that have been considered
originate from flows around aircraft and include three-dimensional
configurations, turbulent and/or transonic regimes, and propulsive jets.
Highly accurate nonlocal artificial boundary conditions have been
obtained using difference potentials method by Ryaben'kii.
This research is a joint effort with
NASA Langley Research Center,
USA. An extended summary for this research area is here.
Combined Implementation of Non-Local ABCs
with the New Generation of Advanced Multigrid Flow Solvers
Based on Factorizable Schemes.
The purpose of this work is to demonstrate that superior performance displayed by each
of the two aforementioned
methods independently can be achieved in the unified framework and
thus improved even further.
Long-Term Numerical Integration of Wave-Type Solutions.
The key feature of the new group of methods that we have proposed
is temporally uniform grid convergence on
arbitrary long time intervals.
This translates into the possibility of building highly accurate
time-dependent artificial boundary conditions
for the numerical study of wave propagation over infinite domains.
Besides, the ABCs appear completely free of any geometric limitations
and do not require grid fitting.
Active Shielding and Control of Environmental Noise.
A new mathematical model for active noise control that eliminates the
need for a reference signal (i.e., knowledge of the specific adverse component
of the acoustic filed to be controlled) and yields the general solution for
control sources. This, in turn, provides a powerful
means for optimization.
Perfectly Matched Layers (PML) for the Helmholtz Equation.
Theoretical and numerical study of the PML (artificial sponge layers designed
to attenuate the outgoing waves after they leave the domain of interest)
for the scalar two-dimensional Helmholtz equation.
Numerical Solution of the Nonlinear Helmholtz Equation.
A fourth-order difference method for the scalar nonlinear Helmholtz equation
that accounts for the phenomena of self-focusing and
backscattering. The method includes special two-way
artificial boundary condition which guarantees the reflectionless propagation of
all outgoing waves and is at the same time capable of correctly prescribing
the incoming (driving) signal.
Applied hydrodynamics (some real life pictures presented)
S. Tsynkov's publications
(fully up to date).
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