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Mixed characteristic discontinuous Galerkin approach for perfect gas dynamics modeling

Journal of Physics: Conference Series 2021年第1期2028卷

作者： V.K. Gatsuk V.V. Lukin Bauman Moscow State Technical University Moscow Russia Keldysh Institute of Applied Mathematics RAS Moscow Russia Ivannikov Institute for System Programming RAS Moscow Russia

The numerical method based on the discontinuous Galerkin (DG) approach for perfect inviscid compressible gas dynamics modelling is developed. The approximate Riemann solvers in combination with gas dynamics equations system characteristic properties are used to calculate the numerical fluxes on the cells interfaces and inside the cells. A number of approximate Riemann solvers are considered. The solution characteristic decomposition is used in the similar to PPML way. The developed algorithm is tested using problems with smooth and discontinuous solutions. Both one-dimensional and two-dimensional test problems are considered. The method provides accurate discontinuity resolution and ability to compute gas-dynamic instabilities with minimal artificial distortion.

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Developing quasi-steady model for studying hemostatic response using supercomputer technologies

Supercomputing Frontiers and Innovations

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Supercomputing Frontiers and Innovations 2018年第4期5卷 67-72页

作者： Trifanov, Petr V. Kaneva, Valeriia N. Strijhak, Sergei V. Panteleev, Mikhail A. Ataullakhanov, Fazoil I. Dunster, Joanne Voevodin, Vadim V. Nechipurenko, Dmitry Y. Department of Physics Lomonosov Moscow State University Moscow Russia Dmitry Rogachev National Research Center of Pediatric Hematology Oncology and Immunology Moscow Russia Center for Theoretical Problems of Physicochemical Pharmacology Moscow Russia Ivannikov Institute for System Programming of the RAS Moscow Russia Faculty of Biological and Medical Physics Moscow Institute of Physics and Technology Dolgoprudny Russia Institute for Cardiovascular and Metabolic Research School of Biological Sciences University of Reading Berkshire United Kingdom Research Computing Center of Lomonosov Moscow State University Moscow Russia

Formation of the platelet plug represents a primary response to the vessel wall injury, but may also result in vessel occlusion. The decrease of the local blood flow due to platelet thrombus formation may lead to serious complications, such as ischemic stroke and myocardial infarction. However, mechanisms responsible for regulation of thrombus dynamics are not clear. In order to get a deeper insight into the role of blood flow and platelet interactions in the formation of the primary platelet plug we developed a particle-based model of microvascular thrombosis using quasisteady flow approximation. In order to simulate thrombus dynamics at physiologically relevant timescales of several minutes, we took advantage of the supercomputer technologies. Our in silico analysis revealed the importance of platelet size heterogeneity for describing experimental data on microvascular thrombus formation. Thus, our model represents a useful tool for the supercomputeraided computational analysis of thrombus dynamics in the microvessels on physiologically relevant timescales. © The Author 2018.

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Numerical simulation of compressible gas flows using regularized gas dynamic equations solver QGDFoam

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AIP Conference Proceedings 2018年第1期2027卷

作者： M. V. Kraposhin T. G. Elizarova M. A. Istomina D. A. Ryazanov K. A. Vatutin 1Ivannikov Institute for System Programming of RAS Moscow Russia 2Keldysh Institute of Applied Mathematics of RAS Moscow Russia 3Lomonosov Moscow State University Moscow Russia

The work presents results of the application of a new OpenFOAM® solver QGDFoam for the numerical simulation of viscous compressible flows in a wide range of Mach numbers. The new solver is based on the explicit approximation of regularized, or quasi-gas dynamic (QGD) equations. The mixed finite-volume and finite-difference approximation is constructed on unstructured spatial grids with co-located variables storage. The solver has been tested for a number of 1D Riemann problems (Sod’s problem, Noh test and others) and 2D cases (Mach 3 forward step, Ladenburg supersonic jet flow with Mach reflection, NASA Langley supersonic overexpanded jet flow and subsonic laminar flow over a backward-facing step). Results of numerical simulations were compared with analytic solutions and OpenFOAM® implementation of the Kurganov-Tadmor scheme, known as rhoCentralFoam. The testing procedure has shown that whereas QGD algorithm is more diffusive than Godunov-type methods with 2nd order TVD schemes with limiters, it is far less diffusive compared with pure upwind schemes as HLL. It was shown that OpenFOAM implementation of the QGD algorithm allows to compute successfully subsonic, sonic and supersonic flows, while other OpenFOAM® solvers have a very limited operational Mach number range. Preliminary results of QGDFoam application for large-scale 3D problems are presented. Scaling tests for up to 768 cores showed good scalability of QGDFoam solver.

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Study of aerophysical processes in the wind farm of the Republic of Adygey

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AIP Conference Proceedings 2021年第1期2351卷

作者： A. V. Ivanov S. V. Strijhak 1)Ivannikov Institute for System Programming of the Russian Academy of Sciences (ISP RAS) 109004 Moscow Russia 2)M. V. Keldysh Institute of Applied Mathematic of the Russian Academy of Sciences (KIAM RAS) 125047 Moscow Russia

The article presents numerical modeling of meteorological processes in the wind farm of the Republic of Adygea. The wind farm has 60 wind turbines, the capacity of each wind turbine is 2.5 MW. A test configuration with 4 nested domains was developed to study the wind farm. The computations were carried out using the WRF-ARW computational code with the wind turbine parameterization module. The calculation was performed for the period 01.04.2020 00:00 – 01.05.2020 00:00 UTC. As a result, the dimensions of the wake formed by the wind farm were obtained, and the influence of the parameterization of wind turbines on the wind distribution calculation was shown. The potential vortex wake can reach sizes up to 15 km. The losses of generated power can reach 1 MW inside the vortex wake. The computations were run on high performance cluster UNIHUB of ISP ras.

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Exact solutions of boundary integral equation arising in vortex methods for incompressible flow simulation around elliptical and Zhukovsky airfoils

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Journal of Physics: Conference Series 2019年第1期1348卷

作者： Kseniia Kuzmina Ilia Marchevsky Evgeniya Ryatina Ivannikov Institute for System Programming of the RAS Alexander Solzhenitsyn st. 25 Moscow 109004 Russia Bauman Moscow State Technical University 2-nd Baumanskaya st. 5 Moscow 105005 Russia

The problem of 2D incompressible flow simulation around airfoils using vortex methods is considered. An exact solution for the boundary integral equation with respect to a free vortex sheet intensity at the airfoil surface line that arises in such problems is obtained. The exact solution is constructed for flows around elliptical and Zhukovsky airfoils using the theory of complex potentials and conformal mappings technique. It is possible to take into account the influence of singularities in the flow domain — point vortices which simulate vortex wake. The obtained exact solutions can be used to verify and estimate the accuracy of numerical schemes for the boundary integral equation solution: such procedure is also described in details.

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Cost-Efficient Numerical Schemes for the Boundary Integral Equation Solution in 2D Vortex Methods

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Journal of Physics: Conference Series 2019年第1期1348卷

作者： Kseniia Kuzmina Ilia Marchevsky Victoriya Moreva Evgeniya Ryatina Ivannikov Institute for System Programming of the RAS Alexander Solzhenitsyn st. 25 Moscow 109004 Russia Bauman Moscow State Technical University 2-nd Baumanskaya st. 5 Moscow 105005 Russia

The problem of the flow simulation around airfoils using Lagrangian vortex methods is considered. Numerical schemes of the second order of accuracy for free vortex sheet intensity distribution along the airfoil are developed for smooth and non-smooth airfoils. The schemes are based on the Galerkin approach with piecewise-constant and piecewise-linear basis functions. The finite element method ideas are used and the resulting piecewise-linear scheme has the same numerical complexity as the scheme with piecewise-constant numerical solution. The modification of a FEM-type scheme is developed for non-smooth airfoils which permits to take into account the discontinuity of the solution at the specified points; its computational cost increases insignificantly.

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On estimates of computational complexity and error of the fast algorithm in the vortex methods

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Journal of Physics: Conference Series 2020年第1期1614卷

作者： K S Kuzmina V S Moreva Bauman Moscow State Technical University 105005 Russia Moscow 2nd Baumanskaya str. 5 Ivannikov Institute for System Programming of the RAS 109004 Russia Moscow Alexander Solzhenitsyn st. 25

One of the efficient ways to speedup calculations in the vortex method, namely the Barnes – Hut-type algorithm, is considered. This method is based on the introducing of a hierarchical structure of domains (binary tree), which allows one to take into account approximately mutual influences of clusters of vortex elements located far from each other when calculating convective velocities. Estimates of the computational complexity of the algorithm for convective velocities calculating are derived, as well as estimates of the error, which depend on the parameters of the algorithm. In practice, these estimates make it possible to choose optimal values of the algorithm parameters and to achieve the maximal speedup of calculations at a given level of acceptable calculation error.

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RKDG method for 2D gas dynamics simulation on uniform rectangular meshes

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Journal of Physics: Conference Series 2019年第1期1348卷

作者： Victoria Korchagova Ivan Fufaev Vladimir Lukin Ilia Marchevsky Sofya Sautkina Bauman Moscow State Technical University 2-nd Baumanskaya st. 5 Moscow 105005 Russia Ivannikov Institute for System Programming of the RAS Alexander Solzhenitsyn st. 25 Moscow 109004 Russia Keldysh Institute of Applied Mathematics RAS Miusskaya sq. 4 Moscow 125047 Russia

This paper is devoted to a numerical simulation of 2D gas dynamics flows on uniform rectangular meshes using the Runge - Kutta - Discontinuous - Galerkin (RKDG) method. The RKDG algorithm was implemented with in-house C++ code based on the experience in the investigation of 1D case. The advantage of the RKDG method over the most popular finite volume method (FVM) is discussed: three basis functions being applied in the framework of the RKDG approach lead to a considerable decrease of the numerical dissipation rate with respect to FVM. The results of the acoustic pulse simulation on a sufficiently coarse mesh with the piecewise-linear approximation show a good agreement with the analytical solution in contrast to the FVM numerical solution. For the Sod problem, the results of the discontinuities propagation illustrate the dependence of the scheme resolution on the numerical fluxes, troubled cell indicator and the limitation technique choice. The possibility to resolve strong shocks is demonstrated with the Sedov cylindrical explosion test.

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Preface

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CEUR Workshop Proceedings 2019年 2514卷 1-2页

作者： Avetisyan, Arutyun Ivar, Jacobson Pozin, Boris A. Petrenko, Alexander K. Pozin, Boris A. Petrenko, Alexander K. Cavalli, Ana Rosa Petrenko, Alexander K. Avetisyan, Arutyun Arlazarov, Vladimir Avdoshin, Sergey Batovrin, Victor K. Bershadsky, Alexander M. Boichenko, Alexander Juris, Borzovs Vasenin, Valery A. Schlingloff, Holger Kalyanov, Georgy Kantorovich, Georgy G. Korolev, Anton Kosolapov, Mikhail S. Kostogryzov, Andrey I. Koznov, Dmitry V. Kuznetsov, Sergey Prokhorov, Sergei Soyfer, Victor A. Starykh, Vladimir A. Stolyarov, Gennady K. Stupnikov, Sergey A. Telnov, Yury Ph. Shmid, Alexander Mira, Kajko-Mattssen Miroslawa Wentzl, Wilfried Mayer, Walter H. Yevtushenko, Nina Zakharov, Victor Zmeev, Oleg Cavalli, Ana Rosa Petrenko, Alexander K. Pozin, Boris A. RAS ISP Russia Ivar Jacobson International Switzerland NRU HSE «-leasing» Co Russia NRU HSE ISP RAS Russia Information and Analytical Systems «-leasing» Co Russia Department of Network Software TELECOM and Management SudParis France NRU HSE Russia Software Engineering of Ivannikov Institute for System Programming RAS Russia RAS System Analysis Institute of Federal Research Centre Informatics and Management Russia Russia Penza State University Russia Federal State Educational Centre of Higher Learning «Plekhanov Russian University of Economics» Russia CISA Academy of Sciences of Latvia State University of Latvia Latvia MSU Institut für Offene Kommunikationssysteme FOKUS Germany Verifikation und Testtheorie an der Humboldt-Universität zu Berlin Germany Institute of Control Sciences RAS Russia Institute of Sociology RAS NRU HSE Russia ISO IEEC Institute of Informatics Problems Federal Research Centre IM RAS Russia St. Petersburg State University Russia Institute for System Programming RAS Moscow State University Russia SRI Korolev Samara State Aerospace University Russia Belarus FRC IM RAS Russia FSEC «Plekhanov Russian University of Economics» Russia KTH School of Information and Communication Technology Sweden Governmental Agricultural Analyst Austria Austria Ivannikov Institute for System Programming RAS Russia Institute of Informatics Problems Federal Research Centre IM RAS Russia Tomsk State University Russia

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Numerical modelling of two-dimensional perfect gas flows using RKDG method on unstructured meshes

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AIP Conference Proceedings 2018年第1期2027卷

作者： V. N. Korchagova I. N. Fufaev V. V. Lukin S. M. Sautkina Applied mathematics dep. Bauman Moscow State Technical University 2-nd Baumanskaya st. 5 Moscow 105005 Russia Ivannikov Institute for System Programming of the RAS Alexander Solzhenitsyn st. 25 Moscow 109004 Russia Keldysh Institute of Applied Mathematics Miusskaya sq. 4 Moscow 125047 Russia

This paper is devoted to the simulation of the two-dimensional gas flows with oscillations and discontinuities using the Runge — Kutta Discontinuous Galerkin (RKDG) method, that has been implemented in the code prototype written in C++. It implements the HLLC numerical flux, the KXRCF troubled cells indicator, the WENO S limiter with the local characteristic decomposition approach and algorithm of dynamic time step control. The computations could be performed on unstructured meshes with mixed cell types (quadrangular and triangular) which can be built in any mesh bulder in IDEAS UNV format (i.e. SALOME). The code is verified on the common numerical tests such as pulsating and vibrating cylinders, Sod-like cylindrical explosion, forward-facing step, blast wave problem. Comparison between analytical solution and numerical results obtained with the in-house code and the open-source OpenFOAM package is presented.

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