Article

Article title NUMERICAL MODELING OF ARCTIC PROBLEMS USING GRID-CHARACTERISTIC METHOD
Authors A.V. Favorskaya, I.B. Petrov, N.I. Khokhlov, D.I. Petrov
Section SECTION III. THE USE OF SUPERCOMPUTER TECHNOLOGIES
Month, Year 12, 2014 @en
Index UDC 519.6
DOI
Abstract Currently the attention to development of Russian Arctic shelf occurs because of the need of seismic prospecting and subsequent digging of hydrocarbon deposits. It should be noted that seismic prospecting in shelf areas of the Arctic has a number of features, among which the presence of a layer of water and ice layer is. In this paper using grid-characteristic method numerical modeling of wave processes in acoustic and elastic media is made which includes shelf seismic prospecting. We consider problem definition, in which there are water, sea ground and the hydrocarbon layer, and another problem definition, in which there are ice, water, sea ground and the hydrocarbon layer. We solve systems of equations describing the state of the infinitesimal volume of continuous linear-elastic medium and the system of equations describing the acoustic field. We use grid-characteristic method to correctly take into account all the boundaries and contacts into the integration area. Also for the solutions of these problems the contact conditions at the boundary between the liquid and the solid layers have been developed.

Download PDF

Keywords Grid-characteristic method; the mechanics of deformable solids; wave problems in coupled elastic-acoustic media; marine seismology; fluid-filled crack; structural acoustics.
References 1. Etter P.C. Underwater Acoustic Modelling and Simulation. 3rd ed. London: Spon Press, 2003.
2. Kulikovskiy A.G., Pogorelov N.V., Semenov A.Yu. Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravneniy [Mathematical problems of numerical solution of hyperbolic systems of equations]. Moscow: Fizmatlit, 2001, 608 p.
3. Magomedov K.M., Kholodov A.S. Setochno-kharakteristicheskie chislennye metody [Grid-characteristic numerical methods]. Moscow: Nauka, 1988, 287 p.
4. Ivanov V.D., Kondaurov V.I., Petrov I.B., Kholodov A.S. Raschet dinamicheskogo deformirovaniya i razrusheniya uprugoplasticheskikh tel setochno-kharakteristicheskimi metodami [The calculation of the dynamic deformation and fracture of elastic-plastic solids grid-characteristic methods], Matemematicheskoe modelirovanie [Matematicheskoe modeling], 1990, Vol. 2, No. 11, pp. 10-29.
5. Favorskaya A.V., Petrov I.B., Sannikov A.V., Kvasov I.E. Grid Characteristic Method Using High Order Interpolation on Tetrahedral Hierarchical Meshes with a Multiple Time Step, Mathematical Models and Computer Simulations, 2013, Vol. 5, No. 5, pp. 409-415.
6. Golubev V.I., Petrov I.B., Khokhlov N.I. Chislennoe modelirovanie seysmicheskoy aktivnosti setochno-kharakteristicheskim metodom [Numerical modeling of seismic activity grid-characteristic method], Zhurnal vychisl. matematiki i matem. fiziki [Journal vychislimoi mathematics and mathematical physics], 2013, Vol. 53, No. 10, pp. 1709-1720.
7. Novatskiy V.K. Teoriya uprugosti [Elasticity theory]. Moscow: Izd-vo Mir, 1975, 872 p.
8. Landau L.D., Lifshits E.M. Teoreticheskaya fizika [Theoretical physics], Vol. 7. Moscow: Nauka Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1987.
9. Harten Ami. High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, 1997, Vol. 135 (2), pp. 260-278.
10. Petrov I.B., Khokhlov N.I. Sravnenie TVD-limiterov dlya chislennogo resheniya uravneniy dinamiki deformiruemogo tverdogo tela setochno-kharakteristicheskim metodom [Comparison TVD-limiters for the numerical solution of the equations of the dynamics of deformable solids grid-characteristic method], Matematicheskie modeli i zadachi upravleniya: Sbornik nauchnykh trudov [Mathematical models and control problems: Proceedings of the], 2011, pp. 104-111.
11. Roe P.L. Characteristic-Based Schemes for the Euler Equations, Annual Review of Fluid Mechanics, 1986, No. 18, pp. 337-365.
12. Novikov Yu.N., Gazhula S.V. Osobennosti otsenki mestorozhdeniy uglevodorodnogo syr'ya arkticheskogo shel'fa Rossii i ikh pereotsenki v sootvetstvii s novoy klassifikatsiey zapasov [Estimation of hydrocarbon deposits on the Arctic shelf of Russia and their revaluation in accordance with the new classification of reserves], Neftegazovaya tekhnologiya. Teoriya i
praktika [Oil and gas technology. Theory and practice], 2008, No. 3. Available at: http://www.ngtp.ru.

Comments are closed.