A Guide to the Russian Academy of Sciences - University of Texas ...

allows sometimes to obtain essential energy economy comparatively to the
traditional ways of the compression control. There were constructed and reasoned
the asymptotic expansions of the solutions of boundary value problems for elliptic
equations with a small parameter on the highest derivatives in the case when
degenerate operator was of the first order and the region boundary was piece wise
smooth. There were also built the asymptotic expansions of fundamental solution of
the Cauchy problem for parabolic equation with lowest terms.
In the sphere of a new numerical methods of the complex multidimensional problems
calculation development there were advanced the following directions.
There were wrought the effective numerical methods and there were created: two large
programs (MOPS-2 and ADAPTATSYA) for calculation of the optimal curvilinear
difference grids in two-dimensional domains of a complex shape. Among them are
the grids adaptive to the peculiarities of solutions in boundary problems. The
feature of this method is the special formalization of the criterion of the closeness of
the grids to uniform ones, which allow to construct effective and stable procedures
to build regular grids with good approximate properties in the very complex twodimensional
regions.
The method and corresponding program complex which were built in order to calculate the
stationary subsonic flows of the gas in axisymmetric channels allow to calculate
flows of a compressible gas in the very complex channels in a wide range of the
Much number when the closed vortex zones occur.
There were offered new effective methods of the Monte Carlo type for solving nonlinear
Boltzmann equations without using of space-time grids. There were built the
difference schemes possessing the uniform convergence on perturbation parameter
for classes of linear and nonlinear singular perturbation differential equations.
There were wrought the difference methods and program MODAMS for calculations of
stationary spatial flow about complex shape bodies (particularly - in the transonic
range of velocities) and following blast diffraction by bodies.
Now the methods of mathematical simulation are developing in the DAP in order to
optimize processes in gas and fluid mechanics. One proposes to calculate gas
dynamic processes with limits on economy, energy expenditure and other
parameters using this and new analytical and numerical approaches.
More then 250 scientific articles were published by the DAP employees.
Function Approximation Theory Department (DFAT)
Approximation and Applications Department (DAA)
Personnel:
Badkov Vladimir Mikhailovich
Berdyshev Vitalii Ivanovich
Gabushin Vladislav Nikolaevich
Koshcheev Viktor Alekseevich
Marinov Anatolii Viacheslavovich
Matveev Oleg Vladimirovich
Petrak Larisa Vladimirovna
Shevaldin Valerii Trifonovich
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