Igor Menshov - Academia.edu (original) (raw)

Papers by Igor Menshov

Research paper thumbnail of Free-boundary method for the numerical solution of gas-dynamic equations in domains with varying geometry

Mathematical Models and Computer Simulations, 2014

A novel method is proposed for numerical solution of gas-dynamic equations on stationary Cartesia... more A novel method is proposed for numerical solution of gas-dynamic equations on stationary Cartesian grids in domains containing solid impermeable and, in the general case, moving inclusions (objects). The suggested technique is based on the immersed boundary method, in which the computational domain (including solid objects) is covered by a single Cartesian grid and the calculation is carried out by the shock-capturing method over all cells. Under this approach, the influence of the solid inclusions on the flow of the gas medium is simulated by the introduction of specially selected mass, momentum, and energy fluxes into the right-hand side of the equations. The currently developed methods for the solution of this class of problems are surveyed and the advantages of the proposed approach are discussed. The method is verified by calculating some test problems that admit analytical solutions and it is used to solve the problem of supersonic flow around a blunt body. The results are compared with the calculation findings based on the standard curvilinear grid tied to the geometry of the body.

Research paper thumbnail of Численное моделирование динамических процесcов в среде мелкодисперсных твердых частиц

Математическое моделирование

Рассматривается модельная система уравнений движения ансамбля твердых частиц, возникающая при кон... more Рассматривается модельная система уравнений движения ансамбля твердых частиц, возникающая при континуальном описании двухфазных дисперсных сред. Особенности системы состоят в наличии разрыва скорости распространения слабых возмущений в фазе частиц при объемной доле плотной упаковки и возможности формирования вакуумных областей, свободных от частиц. Предлагается модификация метода Годунова на основе точного решения задачи Римана и приближенного HLL решения. Тестирование реализованных методов проводится на серии задач, являющихся аналогами известных газодинамических тестов Сода и Шу-Ошера. Рассматривается также задача о разуплотнении пристеночного слоя сжатых частиц. Описывается механизм отрыва частиц от стенки и формирование пристеночной вакуумной области. Результаты численных расчетов сравниваются с имеющимися аналитическими данными.

Research paper thumbnail of On Defragmentation Algorithms for GPU-Native Octree-Based AMR Grids

Lecture Notes in Computer Science, Sep 13, 2021

Research paper thumbnail of Increasing the accuracy of the Godunov scheme for calculating stationary supersonic gas flows based on the solution of the generalized Riemann problem

Computational Mathematics and Mathematical Physics, 1992

Research paper thumbnail of Algorithm of local mesh adaptation based on wavelet analysis with the use of free boundary method

Research paper thumbnail of Estimation of typical frequencies of pressure pulsations in a flow over a rectangular cavity

Research paper thumbnail of On Defragmentation Algorithms for GPU-Native Octree-Based AMR Grids

Lecture Notes in Computer Science, 2021

Research paper thumbnail of GPU-Aware AMR on Octree-Based Grids

Lecture Notes in Computer Science, 2019

Algorithms for refinement/coarsening of octree-based grids entirely on GPU are proposed. Correspo... more Algorithms for refinement/coarsening of octree-based grids entirely on GPU are proposed. Corresponding CUDA/OpenMP implementations demonstrate good performance results which are comparable with p4est library execution times. Proposed algorithms permit to perform all dynamic AMR procedures on octree-based grids entirely in GPU as well as solver kernels without exploiting CPU resourses and pci-e bus for grid data transfers.

Research paper thumbnail of Using the composite Riemann problem solution for capturing interfaces in compressible two-phase flows

Applied Mathematics and Computation, 2019

The paper addresses a novel interface-capturing approach for two-phase flows governed by the five... more The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation model. In this model, two fluids separated with an interface are treated as a homogenous fluid with a characteristic function (volume fraction) determining the location of the fluids and the interface. To suppress the numerical diffusion of the interface, we reconstruct the discontinuity of the volume fraction in each composite (mixed) cell that contains two materials. This sub-cell reconstruction gives rise to the Composite Riemann Problem (CRP) whose solution is used to calculate the numerical flux through cell faces which bound mixed cells. The HLLC method is incorporated to approximate the solution of the CRP. The CRP method is shown to reduce the interface numerical diffusion without introducing spurious oscillations. Its performance and robustness is examined by a variety of 1D and 2D numerical tests, such as the shock-bubble interaction problem, the triplepoint problem, and the Richtmyer-Meshkov instability problem.

Research paper thumbnail of Increasing the order of approximation of Godunov's scheme using solutions of the generalized riemann problem

USSR Computational Mathematics and Mathematical Physics, 1990

12. GRYN V.I., The inverse problem of dynamics of a radiating gas under conditions of axial symme... more 12. GRYN V.I., The inverse problem of dynamics of a radiating gas under conditions of axial symmetry. In: Proceedings of the Seminar on "Numerical Methods for Solving the Transport Equation", 20-23, March 1986. Tartu, 52-59, 1986. GRYN V.I., ZUBOV V.I. and KRIVTSOV V.M., Numerical solution of the inverse problem of dynamics of a radiating gas under conditions of axial symmetry. Zh. Vychisl. Mat. Mat. Fiz., 27, 7, 1078-1084, 1987. GRYN V.I., Direct and inverse problems of the dynamics of a radiating gas. Doctorate Dissertation, Vychisl. Tsentr, Akad. Nauk SSSR, Moscow, 1988. GRYN V.I., On inverse problems of radiative transfer theory in two-dimensional geometries. Zh. Vychisl. Mat. Mat. Fiz., 27, 3, 441-455, 1987. GRYN V.I., Inverse three-dimensional problems of radiative transfer theory similar to the two-dimensional planar and cylindrical cases. Zh. Vychisl. Mat. Mat. Fiz., 29, 10, 1480-1491, 1989. BIRKELAND J.W. and OSS J.P., Spatial resolution of the volume emission coefficient in strongly self-absorbing sources of cylindrical symmetry. Appl. Optics, 7, 8, 1635-1639, 1968. PREOBRAZHENSKII N.G. and PIKALOV V.V., Unstable Problems of Plasma Diagnostics, Nauka, Novosibirsk, 1982. ROMANOV V.G., Inverse Problems of Mathematical Physics, Nauka, Moscow, 1984. VLADIMIROV V.S., The Equations of Mathematical Physics, Nauka, Moscow, 1971. VLADIMIROV V.S., Singularities of the solution of the transport equation. Zh. Vychisl. Mat. Mat. Fiz., 8, 4, 842-852, 1968. FEDORYUK M.F., Ordinary Differential Equations, Nauka, Moscow, 1980.

Research paper thumbnail of Increasing the approximation order of the Godunov scheme based on a solution to the generalized Riemann problem

Zhurnal Vychislitelnoi Matematiki I Matematicheskoi Fiziki, Sep 1, 1990

Research paper thumbnail of Numerical Simulation of Aerodynamic Sound by Navier-Stokes/Lenearized Euler Equations Hybrid Method

44th AIAA Aerospace Sciences Meeting and Exhibit, 2006

Research paper thumbnail of Propagation of strong detonation waves in a dispersed mixture

Soviet Physics Doklady, Dec 1, 1982

Research paper thumbnail of Instability Modes Acoustically Excited in Baroclinic Vortices

3rd Theoretical Fluid Mechanics Meeting, 2002

The normal mode linear analysis is applied to investigate stability of a circular compressible vo... more The normal mode linear analysis is applied to investigate stability of a circular compressible vortex with the emphasis of studying the barclinic effect, Le., the effect of entropy stratification of the basic flow on stability properties. The vortex to be studied has a 'Igylor-type velocity distribution. The stratillcation of entropy is modelled by a Gaussian twoparametric profile, whose parameters control the maximal deviation from the homentropic distribution and the extent of the entropic zone. The results presented concern the effect of these parameters and the vortex intensity as well on instability characteristics, as the growth rate and the azimuthal phase frequency. Particularly, the Taylor homentropic vortex is found to be stable for sufficiently high intensities only, and ceases to be stable as the vortex intencity weakens. It is also presented an example situation, where unstable normal modes are excited. This is the scattering of sound waves by the vortex. By simulating this process numerically, we show that the scattered field due to incident of sound waves on the vortex becomes unstable, and takes a typical angular regular structure. The characteristics of this instability, Le., the growth rate and the azimuthal phase frequency coincides with those of unstable normal modes very closely, which definitely indicates the excitation of these normal modes in the sound scattering process. Keyword: Compressible vortex, Linear-stability analysis, Sound scattering

Research paper thumbnail of Variation matrices in the Riemann problem with application to implicit Godunov's method

38th Aerospace Sciences Meeting and Exhibit, 2000

The variational Riemann problem (VRP) is defined as the first variation of the solution to Rieman... more The variational Riemann problem (VRP) is defined as the first variation of the solution to Riemann's initial-value problem, also known as the problem of breakup of an arbitrary discontinuity in a gas, when the initial data undergo small variations. We show that the solution to the VRP can be analytically obtained, provided that the solution to the baseline Riemann problem is known. This solution describes the interaction of two abutting parcels of small disturbances against the background of a given base flow and therefore can be efficiently implemented in numerical methods for aeroacoustics. When the spatial distribution of disturbances and base flow parameters are given at a time moment at mesh points of a computational grid, one can exactly determine the disturbance evolution for a short lapse of time by solving the VRP at mesh interfaces. This can then be applied to update disturbance values to a new time moment by using the standard finite-volume scheme. In other words, the VRP can be used in computational aeroacoustics in the similar way to the Riemann problem used in Godunov-type methods for computational fluid dynamics. The present paper elaborates on this idea and adopts the solution to the VRP as a building block for a finite-volume Godunov-type method for aeroacoustics.

Research paper thumbnail of Constructing parallel numerical model by means of the composition of computational objects

Research paper thumbnail of Parallel Algorithms for an Implicit CFD Solver on Tree-Based Grids

Lecture Notes in Computer Science, 2017

Parallel implementation of the implicit LU-SGS solver is considered. It leads to the graph colori... more Parallel implementation of the implicit LU-SGS solver is considered. It leads to the graph coloring problem. A novel recursive graph coloring algorithm has been proposed that requires only three colors on 2:1 balanced quadtree-based meshes. The algorithm has been shown to allow simple parallel implementations, including GPU architectures, and is fully coherent with local grid coarsing/refining procedures resulting in highly effective co-execution with local grid adaptation.

Research paper thumbnail of The use of free boundary method for solving the problem of the flow past moving bodies

Abstract: The paper is dedicated to the numerical solution of unsteady Euler equations describing... more Abstract: The paper is dedicated to the numerical solution of unsteady Euler equations describing the gas flow past one or several solid nondeformable bodies that can move either according to some law (forced movement) or under the action of the reaction forces from the gas (free movement) using free boundary method.Note: Research direction:Mathematical modelling in actual problems of science and technic

Research paper thumbnail of A Parallel Locally-Adaptive 3D Model on Cartesian Nested-Type Grids

Lecture Notes in Computer Science, 2017

The paper addresses the 3D extension of the Cartesian multilevel nested-type grid methodology and... more The paper addresses the 3D extension of the Cartesian multilevel nested-type grid methodology and its software implementation in an application library written in C++ object-oriented language with the application program interface OpenMP for parallelizing calculations on shared memory. The library accounts for the specifics of multithread calculations of 3D problems on Cartesian grids, which makes it possible to substantially minimize the loaded memory via non-storing the grid information. The loop order over cells is represented by a special list that remarkably simplifies parallel realization with the OpenMP directives. Test results show high effectiveness of dynamical local adaptation of Cartesian grids, and increasing of this effectiveness while the number of adaptation levels becomes larger.

Research paper thumbnail of Interface Capturing Method Based on the Cahn–Hilliard Equation for Two-Phase Flows

Computational Mathematics and Mathematical Physics, 2020

Abstract A numerical method for flows of heterogeneous two-phase compressible media is considered... more Abstract A numerical method for flows of heterogeneous two-phase compressible media is considered. The main problem in the construction of such a method is to find the interface between the components with different physical and mechanical properties. An efficient method for solving this problem that gives a good spatial resolution of the interfaces is proposed. This method is based on the use of the Cahn–Hilliard equation. To describe the flow of the two-phase medium, the single-velocity five-equation model is used; in this model, the Cahn–Hilliard equation is used as the equation for the order function. This makes it possible to significantly decrease the domain of the interface numerical smearing. Numerical results confirm the high accuracy and effectiveness of the proposed method.

Research paper thumbnail of Free-boundary method for the numerical solution of gas-dynamic equations in domains with varying geometry

Mathematical Models and Computer Simulations, 2014

A novel method is proposed for numerical solution of gas-dynamic equations on stationary Cartesia... more A novel method is proposed for numerical solution of gas-dynamic equations on stationary Cartesian grids in domains containing solid impermeable and, in the general case, moving inclusions (objects). The suggested technique is based on the immersed boundary method, in which the computational domain (including solid objects) is covered by a single Cartesian grid and the calculation is carried out by the shock-capturing method over all cells. Under this approach, the influence of the solid inclusions on the flow of the gas medium is simulated by the introduction of specially selected mass, momentum, and energy fluxes into the right-hand side of the equations. The currently developed methods for the solution of this class of problems are surveyed and the advantages of the proposed approach are discussed. The method is verified by calculating some test problems that admit analytical solutions and it is used to solve the problem of supersonic flow around a blunt body. The results are compared with the calculation findings based on the standard curvilinear grid tied to the geometry of the body.

Research paper thumbnail of Численное моделирование динамических процесcов в среде мелкодисперсных твердых частиц

Математическое моделирование

Рассматривается модельная система уравнений движения ансамбля твердых частиц, возникающая при кон... more Рассматривается модельная система уравнений движения ансамбля твердых частиц, возникающая при континуальном описании двухфазных дисперсных сред. Особенности системы состоят в наличии разрыва скорости распространения слабых возмущений в фазе частиц при объемной доле плотной упаковки и возможности формирования вакуумных областей, свободных от частиц. Предлагается модификация метода Годунова на основе точного решения задачи Римана и приближенного HLL решения. Тестирование реализованных методов проводится на серии задач, являющихся аналогами известных газодинамических тестов Сода и Шу-Ошера. Рассматривается также задача о разуплотнении пристеночного слоя сжатых частиц. Описывается механизм отрыва частиц от стенки и формирование пристеночной вакуумной области. Результаты численных расчетов сравниваются с имеющимися аналитическими данными.

Research paper thumbnail of On Defragmentation Algorithms for GPU-Native Octree-Based AMR Grids

Lecture Notes in Computer Science, Sep 13, 2021

Research paper thumbnail of Increasing the accuracy of the Godunov scheme for calculating stationary supersonic gas flows based on the solution of the generalized Riemann problem

Computational Mathematics and Mathematical Physics, 1992

Research paper thumbnail of Algorithm of local mesh adaptation based on wavelet analysis with the use of free boundary method

Research paper thumbnail of Estimation of typical frequencies of pressure pulsations in a flow over a rectangular cavity

Research paper thumbnail of On Defragmentation Algorithms for GPU-Native Octree-Based AMR Grids

Lecture Notes in Computer Science, 2021

Research paper thumbnail of GPU-Aware AMR on Octree-Based Grids

Lecture Notes in Computer Science, 2019

Algorithms for refinement/coarsening of octree-based grids entirely on GPU are proposed. Correspo... more Algorithms for refinement/coarsening of octree-based grids entirely on GPU are proposed. Corresponding CUDA/OpenMP implementations demonstrate good performance results which are comparable with p4est library execution times. Proposed algorithms permit to perform all dynamic AMR procedures on octree-based grids entirely in GPU as well as solver kernels without exploiting CPU resourses and pci-e bus for grid data transfers.

Research paper thumbnail of Using the composite Riemann problem solution for capturing interfaces in compressible two-phase flows

Applied Mathematics and Computation, 2019

The paper addresses a novel interface-capturing approach for two-phase flows governed by the five... more The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation model. In this model, two fluids separated with an interface are treated as a homogenous fluid with a characteristic function (volume fraction) determining the location of the fluids and the interface. To suppress the numerical diffusion of the interface, we reconstruct the discontinuity of the volume fraction in each composite (mixed) cell that contains two materials. This sub-cell reconstruction gives rise to the Composite Riemann Problem (CRP) whose solution is used to calculate the numerical flux through cell faces which bound mixed cells. The HLLC method is incorporated to approximate the solution of the CRP. The CRP method is shown to reduce the interface numerical diffusion without introducing spurious oscillations. Its performance and robustness is examined by a variety of 1D and 2D numerical tests, such as the shock-bubble interaction problem, the triplepoint problem, and the Richtmyer-Meshkov instability problem.

Research paper thumbnail of Increasing the order of approximation of Godunov's scheme using solutions of the generalized riemann problem

USSR Computational Mathematics and Mathematical Physics, 1990

12. GRYN V.I., The inverse problem of dynamics of a radiating gas under conditions of axial symme... more 12. GRYN V.I., The inverse problem of dynamics of a radiating gas under conditions of axial symmetry. In: Proceedings of the Seminar on "Numerical Methods for Solving the Transport Equation", 20-23, March 1986. Tartu, 52-59, 1986. GRYN V.I., ZUBOV V.I. and KRIVTSOV V.M., Numerical solution of the inverse problem of dynamics of a radiating gas under conditions of axial symmetry. Zh. Vychisl. Mat. Mat. Fiz., 27, 7, 1078-1084, 1987. GRYN V.I., Direct and inverse problems of the dynamics of a radiating gas. Doctorate Dissertation, Vychisl. Tsentr, Akad. Nauk SSSR, Moscow, 1988. GRYN V.I., On inverse problems of radiative transfer theory in two-dimensional geometries. Zh. Vychisl. Mat. Mat. Fiz., 27, 3, 441-455, 1987. GRYN V.I., Inverse three-dimensional problems of radiative transfer theory similar to the two-dimensional planar and cylindrical cases. Zh. Vychisl. Mat. Mat. Fiz., 29, 10, 1480-1491, 1989. BIRKELAND J.W. and OSS J.P., Spatial resolution of the volume emission coefficient in strongly self-absorbing sources of cylindrical symmetry. Appl. Optics, 7, 8, 1635-1639, 1968. PREOBRAZHENSKII N.G. and PIKALOV V.V., Unstable Problems of Plasma Diagnostics, Nauka, Novosibirsk, 1982. ROMANOV V.G., Inverse Problems of Mathematical Physics, Nauka, Moscow, 1984. VLADIMIROV V.S., The Equations of Mathematical Physics, Nauka, Moscow, 1971. VLADIMIROV V.S., Singularities of the solution of the transport equation. Zh. Vychisl. Mat. Mat. Fiz., 8, 4, 842-852, 1968. FEDORYUK M.F., Ordinary Differential Equations, Nauka, Moscow, 1980.

Research paper thumbnail of Increasing the approximation order of the Godunov scheme based on a solution to the generalized Riemann problem

Zhurnal Vychislitelnoi Matematiki I Matematicheskoi Fiziki, Sep 1, 1990

Research paper thumbnail of Numerical Simulation of Aerodynamic Sound by Navier-Stokes/Lenearized Euler Equations Hybrid Method

44th AIAA Aerospace Sciences Meeting and Exhibit, 2006

Research paper thumbnail of Propagation of strong detonation waves in a dispersed mixture

Soviet Physics Doklady, Dec 1, 1982

Research paper thumbnail of Instability Modes Acoustically Excited in Baroclinic Vortices

3rd Theoretical Fluid Mechanics Meeting, 2002

The normal mode linear analysis is applied to investigate stability of a circular compressible vo... more The normal mode linear analysis is applied to investigate stability of a circular compressible vortex with the emphasis of studying the barclinic effect, Le., the effect of entropy stratification of the basic flow on stability properties. The vortex to be studied has a 'Igylor-type velocity distribution. The stratillcation of entropy is modelled by a Gaussian twoparametric profile, whose parameters control the maximal deviation from the homentropic distribution and the extent of the entropic zone. The results presented concern the effect of these parameters and the vortex intensity as well on instability characteristics, as the growth rate and the azimuthal phase frequency. Particularly, the Taylor homentropic vortex is found to be stable for sufficiently high intensities only, and ceases to be stable as the vortex intencity weakens. It is also presented an example situation, where unstable normal modes are excited. This is the scattering of sound waves by the vortex. By simulating this process numerically, we show that the scattered field due to incident of sound waves on the vortex becomes unstable, and takes a typical angular regular structure. The characteristics of this instability, Le., the growth rate and the azimuthal phase frequency coincides with those of unstable normal modes very closely, which definitely indicates the excitation of these normal modes in the sound scattering process. Keyword: Compressible vortex, Linear-stability analysis, Sound scattering

Research paper thumbnail of Variation matrices in the Riemann problem with application to implicit Godunov's method

38th Aerospace Sciences Meeting and Exhibit, 2000

The variational Riemann problem (VRP) is defined as the first variation of the solution to Rieman... more The variational Riemann problem (VRP) is defined as the first variation of the solution to Riemann's initial-value problem, also known as the problem of breakup of an arbitrary discontinuity in a gas, when the initial data undergo small variations. We show that the solution to the VRP can be analytically obtained, provided that the solution to the baseline Riemann problem is known. This solution describes the interaction of two abutting parcels of small disturbances against the background of a given base flow and therefore can be efficiently implemented in numerical methods for aeroacoustics. When the spatial distribution of disturbances and base flow parameters are given at a time moment at mesh points of a computational grid, one can exactly determine the disturbance evolution for a short lapse of time by solving the VRP at mesh interfaces. This can then be applied to update disturbance values to a new time moment by using the standard finite-volume scheme. In other words, the VRP can be used in computational aeroacoustics in the similar way to the Riemann problem used in Godunov-type methods for computational fluid dynamics. The present paper elaborates on this idea and adopts the solution to the VRP as a building block for a finite-volume Godunov-type method for aeroacoustics.

Research paper thumbnail of Constructing parallel numerical model by means of the composition of computational objects

Research paper thumbnail of Parallel Algorithms for an Implicit CFD Solver on Tree-Based Grids

Lecture Notes in Computer Science, 2017

Parallel implementation of the implicit LU-SGS solver is considered. It leads to the graph colori... more Parallel implementation of the implicit LU-SGS solver is considered. It leads to the graph coloring problem. A novel recursive graph coloring algorithm has been proposed that requires only three colors on 2:1 balanced quadtree-based meshes. The algorithm has been shown to allow simple parallel implementations, including GPU architectures, and is fully coherent with local grid coarsing/refining procedures resulting in highly effective co-execution with local grid adaptation.

Research paper thumbnail of The use of free boundary method for solving the problem of the flow past moving bodies

Abstract: The paper is dedicated to the numerical solution of unsteady Euler equations describing... more Abstract: The paper is dedicated to the numerical solution of unsteady Euler equations describing the gas flow past one or several solid nondeformable bodies that can move either according to some law (forced movement) or under the action of the reaction forces from the gas (free movement) using free boundary method.Note: Research direction:Mathematical modelling in actual problems of science and technic

Research paper thumbnail of A Parallel Locally-Adaptive 3D Model on Cartesian Nested-Type Grids

Lecture Notes in Computer Science, 2017

The paper addresses the 3D extension of the Cartesian multilevel nested-type grid methodology and... more The paper addresses the 3D extension of the Cartesian multilevel nested-type grid methodology and its software implementation in an application library written in C++ object-oriented language with the application program interface OpenMP for parallelizing calculations on shared memory. The library accounts for the specifics of multithread calculations of 3D problems on Cartesian grids, which makes it possible to substantially minimize the loaded memory via non-storing the grid information. The loop order over cells is represented by a special list that remarkably simplifies parallel realization with the OpenMP directives. Test results show high effectiveness of dynamical local adaptation of Cartesian grids, and increasing of this effectiveness while the number of adaptation levels becomes larger.

Research paper thumbnail of Interface Capturing Method Based on the Cahn–Hilliard Equation for Two-Phase Flows

Computational Mathematics and Mathematical Physics, 2020

Abstract A numerical method for flows of heterogeneous two-phase compressible media is considered... more Abstract A numerical method for flows of heterogeneous two-phase compressible media is considered. The main problem in the construction of such a method is to find the interface between the components with different physical and mechanical properties. An efficient method for solving this problem that gives a good spatial resolution of the interfaces is proposed. This method is based on the use of the Cahn–Hilliard equation. To describe the flow of the two-phase medium, the single-velocity five-equation model is used; in this model, the Cahn–Hilliard equation is used as the equation for the order function. This makes it possible to significantly decrease the domain of the interface numerical smearing. Numerical results confirm the high accuracy and effectiveness of the proposed method.