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Continuum Mechanics Tasks


Preparation of Monograph “Solution Techniques of Continuum Mechanics Multidimensional Problems on Irregular Meshes” to be Published in English

Tech Area / Field

  • PHY-NGD/Fluid Mechanics and Gas Dynamics/Physics

3 Approved without Funding

Registration date

Leading Institute
VNIIEF, Russia, N. Novgorod reg., Sarov


  • Los Alamos National Laboratory, USA, NM, Los-Alamos

Project summary

The goal of the project is to bring together in one book, to systemize and summarize the results of research work, started almost 40 years ago. The book will consist of 6 chapters.

During the last 40 years in RFNC-VNNIEF mathematical department the theoretical principles of irregular methods, realized in MEDUZA and DMK production complexes, have been developed under the direction of two Doctors of Physics and Maths - I.D. Sofronov, and V.V. Rasskazova. These methods have been used for a great number of calculations; they were reported during conferences, published in scientific articles and served as a background during Doctors and Candidates theses defense. Grate interest is shown in this numerical mathematics direction.

This monograph is aimed at description of methods for continuum mechanics tasks solution in two and three-dimensional spaces using finite-difference approach on irregular and regular meshes. Regular and irregular meshes may be used in different parts of task decision regions simultaneously. By means of this methods one may calculate two- (DMK and MEDUZA) and three-dimensional gas-dynamic tasks taking into account material strength properties, heat conductivity, particulate pollutants transfer which are involved into motion by the medium.

The work will suggest original means of desired feature irregular and regular meshes creation in the areas of structure that is complicated enough. Three-dimensional space is supposed to be filled with Dirichlet-Voronoy figures using irregular method or optional convex polyhedrons having no folds and gaps.

DMK and TMK methods are used both as Lagrange form of gas-dynamics equations and difference countable mesh, connected with the substance and moving together with it. To eliminate Lagrange mesh countable distortions the technique that keeps plane and trihedral angles convex is used during the process of numerical experiment as well as mesh local structural readjustment in the form of separate cells splitting or grouping the two neighboring. These techniques will include methods of various matters interfaces movement determination. MEDUZA method is based on Euler’s form of gas-dynamic equations and for its discretization uses meshes, which are not connected with the matter.

The work will be provided with a great number of text tasks, which demonstrate the efficiency and performance capabilities of the methods under consideration.

It is assumed that foreign collaborators will participate in the discussion of the program, work plan and final results.

The monograph will be written by high-qualified specialists in this particular area of science, who contributed a lot to this program creation, development and who nowadays participate in weapon related programs. Presumably the monograph will consist of 10-15 typographical (200-300 A4 format sheets).

The monograph should raise interest of many researchers, engineers and post-graduate students, who specialize in methods of continuum mechanics mathematical simulation.


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