Institute of Numerical Mathematics

Moscow, Russia

Institute of Numerical Mathematics

Moscow, Russia

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Boiko A.V.,Tyumen State Oil and Gas University | Ivanov A.V.,RAS Institute of Theoretical and Applied Mechanics | Kachanov Y.S.,RAS Institute of Theoretical and Applied Mechanics | Mischenko D.A.,RAS Institute of Theoretical and Applied Mechanics | Nechepurenko Y.M.,Institute of Numerical Mathematics
Theoretical and Computational Fluid Dynamics | Year: 2016

A combined theoretical and numerical analysis of an experiment devoted to the excitation of Görtler vortices by localized stationary or vibrating surface nonuniformities in a boundary layer over a concave surface is performed. A numerical model of generation of small-amplitude disturbances and their downstream propagation based on parabolic equations is developed. In the framework of this model, the optimal and the modal parts of excited disturbance are defined as solutions of initial-value problems with initial values being, respectively, the optimal disturbance and the leading local mode at the location of the source. It is shown that a representation of excited disturbance as a sum of the optimal part and a remainder makes it possible to describe its generation and downstream propagation, as well as to predict satisfactorily the corresponding receptivity coefficient. In contrast, the representation based on the modal part provides only coarse information about excitation and propagation of disturbance in the range of parameters under investigation. However, it is found that the receptivity coefficients estimated using the modal parts can be reinterpreted to preserve their practical significance. A corresponding procedure was developed. The theoretical and experimental receptivity coefficients are estimated and compared. It is found that the receptivity magnitudes grow significantly with the disturbance frequency. Variation of the span-wise scale of the nonuniformities affects weakly the receptivity characteristics at zero frequency. However, at high frequencies, the efficiency of excitation of Görtler vortices depends substantially on the span-wise scale. © 2016 Springer-Verlag Berlin Heidelberg


Agouzal A.,University of Lyon | Lipnikov K.,Los Alamos National Laboratory | Vassilevski Y.,Institute of Numerical Mathematics
Proceedings of the 20th International Meshing Roundtable, IMR 2011 | Year: 2011

For a given function, we consider a problem of minimizing the P1 interpolation error on a set of triangulations with a fixed number of triangles. The minimization problem is reformulated as a problem of generating a mesh which is quasi-uniform in a specially designed metric. For functions with indefinite Hessian, we show existence of a family of metrics with highly diverse properties. The family may include both anisotropic and isotropic metrics. A developed theory is verified with numerical examples.


Litsarev M.S.,Skolkovo Institute of Science and Technology | Oseledets I.V.,Skolkovo Institute of Science and Technology | Oseledets I.V.,Institute of Numerical Mathematics
Computer Physics Communications | Year: 2014

We present a new version of the DEPOSIT computer code based on the low rank approximations. This approach is based on the two dimensional cross decomposition of matrices and separated representations of analytical functions. The cross algorithm is available in the distributed package and can be used independently. All integration routines related to the computation of the deposited energy T (b) are implemented in a new way (low rank separated representation format on homogeneous meshes). By using this approach a bug in integration routines of previous version of the code was found and fixed in the current version. The total computational time was significantly accelerated and is about several minutes. New version program summary: Program title: DEPOSIT 2014. Catalogue identifier: AENP_v2_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENP_v2_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU General Public License, version 3. No. of lines in distributed program, including test data, etc.: 182103. No. of bytes in distributed program, including test data, etc.: 1163484. Distribution format: tar.gz. Programming language: C+ +, Fortran. Computer: Any computer that can run C+ + and Fortran compilers. Operating system: Any operating system with installed compilers mentioned above. Tested on Mac OS X 10.9 and Ubuntu 12.04. Has the code been vectorized or parallelized?: Due to the fast computation in the current implementation only a single-threaded version has been developed. Classification: 2.6, 4.10, 4.11, 19.1. External routines: BLAS, LAPACK and ALGLIB. The last one is included in the distribution. Catalogue identifier of previous version: AENP_v1_0. Journal reference of previous version: Comput. Phys. Comm. 184(2013) 432. Does the new version supersede the previous version?: Yes. Nature of problem:. For a given impact parameter b to calculate the deposited energy T (b) as a 3D integral over a coordinate space, and ionization probabilities Pm (b). For a given energy of the projectile to calculate the total and m-fold electron-loss cross sections using T (b) values on the whole b-mesh. Solution method:. Calculation of the 3D-integral T (b) in all points of the b-mesh based on the low rank separated representations of matrices and tensors. For details, please see Ref. [1]. Reasons for new version:. The computation of the deposited energy T (b) integral is the slowest part of the program and should be done as fast as possible. To accelerate the program a new approach based on the low rank approximations was applied. It made computational scheme more stable and decreased the computational time by a factor of ∼ 103. By means of this approach a bug in the integration routines was found and fixed for a special case of the energy gain. Summary of revisions:. A two dimensional cross decomposition algorithm was developed as an independent module and was integrated with the energy gain Δ E. For the Slater density ρ (r) a separated representation via a sum of Gaussians was implemented. The calculation of three dimensional integrals T (b) was totally rewritten by using quadrature schemes based on the cross decomposition for energy gain and separated representations for Slater density. Details are reported in Ref. [1]. Running time:. For a given energy the total and m-fold cross sections are calculated within about several minutes on a single-core. References: [1] M.S. Litsarev, I.V. Oseledets. Fast computation of the deposited energy integrals with the low-rank approximation technique, Computational Science and Discovery 2014 (submitted); arXiv:1403.4068. © 2014 Elsevier B.V. All rights reserved.


Ivchenko V.O.,UK National Oceanography Center | Sinha B.,UK National Oceanography Center | Zalesny V.B.,Institute of Numerical Mathematics | Marsh R.,UK National Oceanography Center | Blaker A.T.,UK National Oceanography Center
Journal of Physical Oceanography | Year: 2013

An integral constraint for eddy fluxes of potential vorticity (PV), corresponding to global momentum conservation, is applied to two-layer zonal quasigeostrophic channel flow. This constraint must be satisfied for any type of parameterization of eddy PV fluxes. Bottom topography strongly influences the integral constraint compared to a flat bottom channel. An analytical solution for the mean flow solution has been found by using asymptotic expansion in a small parameter, which is the ratio of the Rossby radius to the meridional extent of the channel. Applying the integral constraint to this solution, one can find restrictions for eddy PV transfer coefficients that relate the eddy fluxes of PV to the mean flow. These restrictions strongly deviate from restrictions for the channel with flat bottom topography. © 2013 American Meteorological Society.


Achatz U.,Goethe University Frankfurt | Lobl U.,Goethe University Frankfurt | Lobl U.,Institute of Numerical Mathematics | Dolaptchiev S.I.,Goethe University Frankfurt | Gritsun A.,Goethe University Frankfurt
Journal of the Atmospheric Sciences | Year: 2013

Climate-system models use a multitude of parameterization schemes for small-scale processes. These should respond to externally forced climate variability in an appropriate manner so as to reflect the response of the parameterized process to a changing climate. The most attractive route to achieve such a behavior would certainly be provided by theoretical understanding sufficiently deep to enable the a priori design of climate-sensitive parameterization schemes. An alternative path might, however, be helpful when the parameter tuning involved in the development of a scheme is objective enough so that these parameters can be described as functions of the statistics of the climate system. Provided thatthe dynamics of the process in question is sufficiently stochastic, and that the external forcing is not too strong, the fluctuation-dissipation theorem (FDT) might be a tool to predict from the statistics of a system (e.g., the atmosphere) how an objectively tuned parameterization should respond to external forcing (e.g., by anomalous sea surface temperatures). This problem is addressed within the framework of low-order (reduced) models for barotropic flow on the sphere,based on a few optimal basis functions and using an empirical linear subgrid-scale (SGS) closure. A reduced variant of quasi-Gaussian FDT (rqG-FDT) is used to predict the response of the SGS closure to anomalous local vorticity forcing. At sufficiently weak forcing, use of the rqG-FDT is found to systematically improve the agreement between the response of a reduced model and that of a classic spectral code for the solution of the barotropic vorticity equation. © 2013 American Meteorological Society.


Vassilevski Y.,Institute of Numerical Mathematics
Engineering with Computers | Year: 2010

In the adaptive mesh generation, the space mesh should be adequate to the surface mesh. When the analytical surface representation is not known, additional surface information may be extracted from triangular surface meshes. We describe a new surface reconstruction method which uses approximate Hessian of a piecewise linear function representing the discrete surface. Efficiency of the proposed method is illustrated with two CFD applications. © Springer-Verlag London Limited 2009.


Oseledets I.,Institute of Numerical Mathematics
IEEE Transactions on Computers | Year: 2011

It is well known that Chinese Remainder Theorem (CRT) can be used to construct efficient algorithms for multiplication of polynomials over GF(2). In this note, we show how to select an appropriate set of modulus polynomials to obtain minimal number of multiplications. © 2011 IEEE.


Tromeur-Dervout D.,Camille Jordan Institute | Vassilevski Y.,Institute of Numerical Mathematics
Lecture Notes in Computational Science and Engineering | Year: 2011

Efficient choice of the initial guess for the iterative solution of series of systems is considered. The series of systems are typical for unsteady nonlinear fluid flow problems. The history of iterative solution at previous time steps is used for computing a better initial guess. This strategy is applied for two iterative linear system solvers (GCR and GMRES). A reduced model technique is developed for implicitly discretized nonlinear evolution problems. The technique computes a better initial guess for the inexact Newton method. The methods are successfully tested in parallel CFD simulations. The latter approach is suitable for GRID computing as well. © 2010 Springer.

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