Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy
The present paper addresses the numerical method for solving the gas dynamics equations that has ... more The present paper addresses the numerical method for solving the gas dynamics equations that has been proposed by S. K. Godunov almost 60 years ago. The method reads as a first-order explicit finite-volume scheme with the numerical flux approximation based on the exact solution to the Riemann problem. We consider the extension of the Godunov method to an unconditionally stable second-order accurate implicit-explicit time marching scheme, introduce the variational Riemann problem (VRP), and discuss possible applications of this problem to solving the hybrid implicit-explicit Godunov scheme and also problems of aeroacoustics.
The paper addresses a two-temperature model for simulating compressible two-phase flow taking int... more The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase Baer-Nunziato model in the limit of complete velocity relaxation and consists of the phase mass and energy balance equations, the mixture momentum equation, and a transport equation for the volume fraction. Terms describing effects of mechanical relaxation, temperature relaxation, and thermal conduction on volume fraction evolution are derived and demonstrated to be significant for heat conduction problems. The thermal conduction leads to instantaneous thermal relaxation so that the temperature equilibrium is always maintained in the interface region with meeting the entropy relations. A numerical method is developed to solve the model governing equations that ensures the pressure-velocitytemperature (PVT) equilibrium condition in its high-order extension. We...
Two-Phase Flow Modeling for Gas-Solid Granular Mixtures in Dense and Dilute Concentration
We consider modelling gas-solid granular mixture flow in a wide range of solid volume fractions. ... more We consider modelling gas-solid granular mixture flow in a wide range of solid volume fractions. In such flows, concentration of the solid phase changes from dilute (low concentration) to dense (high concentration). Several macroscopic phenomenological models have been developed for gas-solid granular medium. The 6-wave 7-equation Baer-Nunziato model (BN) has been designed for gas-solid granular mixtures with dense concentration of the solid phase. Dilute mixtures are commonly modeled with the one-pressure model that is not hyperbolic in the whole range of model parameters. In the paper we are concerned with the problem of combaining the two models. We develop a new model of two-phase compressible flows which is hyperbolic and thermodynamically consistent and covers a wide range of solid phase concentrations in an unique approach. We tets the proposed model on several problems where the flow regime is changed from dilute to highly packed mixtures. The numerical calculations are carr...
An interface-regularizing model for compressible three-fluid flows with interfacial tensions
Computers & Fluids
Abstract We present a diffuse-interface model for simulating compressible three-fluid flows with ... more Abstract We present a diffuse-interface model for simulating compressible three-fluid flows with surface tension. In this model different fluids are separated with resolved interfaces. We first deduce the jump conditions across the material interfaces under surface tension. The interfaces are represented with the advection equations for volume fractions. Traditional methods for solving these equations result in serious numerical smearing of interface surfaces. To minimize this numerical effect, we introduce mathematical regularization of the governing equations by implementing an artificial compression method. The mathematical regularization is introduced in such a way that the jump conditions across the material interface maintain unaltered. Further we demonstrate that for the three-fluid formulation the direct implementation of the artificial compression method for each volume fraction can violate the non-negativity constraints for volume fractions. To cope with this problem, we propose a simple and robust method to ensure the volume fraction constraints. In this method instead of the original advection equations for volume fractions, we solve the advection equation with an additional compression term for new characteristic functions in the form of non-linear combinations of volume fractions. Moreover, a HLLC solver for solving the model equations is developed. The numerical results of several benchmark problems display the efficiency of the proposed algorithm.
Abstract. In the present paper we consider an Eulerian numerical method for calculating multi-mat... more Abstract. In the present paper we consider an Eulerian numerical method for calculating multi-material fluid. This method relates to the class of interface capturing methods that resolve material interfaces not exactly, but with some numerical smearing in space. To suppress this numerical smearing, we suggest a numerical flux approximation based on the sub-cell material interface reconstruction by simple patterns and the solution of the composite Riemann problem (CRP). It is found that the improved scheme captures the interface within one computational cell in 1D calculations. For multi-dimensional calculations we implement an approach of directional splitting that sufficiently decreases smearing of material interfaces what is demonstrated in computations of various multi-material applications.
High-performance parallel calculations of helical instability in supersonic jets
Book of abstracts of the Japan-Russia workshop on hydrodynamical instability and turbulence, Kobe... more Book of abstracts of the Japan-Russia workshop on hydrodynamical instability and turbulence, Kobe, Nov.16-23 2008, p. 23.
The present paper is concerned with a numerical model that is developing to simulate dynamical pr... more The present paper is concerned with a numerical model that is developing to simulate dynamical processes in a heterogeneous two-phase medium consisting of two components – elastic-plastic porous solid and gas that occupies the domain in between of the solid. The scope of our interest is regimes of large deformations and intense loading-unloading processes when the solid and the gas have different velocities and temperatures, i.e., are in dynamical and thermal non-equilibrium. Such a model needs to describe, for example, combustion and detonation in condensed porous explosives that are manufactured by pressing granular propellants.
Parallel Algorithms for an Implicit CFD Solver on Tree-Based Grids
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.
A Parallel Locally-Adaptive 3D Model on Cartesian Nested-Type Grids
Lecture Notes in Computer Science
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.
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.
Theoretical and numerical analysis of density perturbation development induced by high velocity impact
Physics of Fluids
The problem of high velocity impact between two solid plates where one of them has a non-uniforml... more The problem of high velocity impact between two solid plates where one of them has a non-uniformly disturbed density field is studied. The nature of an initial perturbation here differs from one co...
О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к ... more О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к а д е м и и н а у к И.В.Семёнов, И.С.Меньшов, М.Ю.Немцев Математическое моделирование осесимметричных внутрибаллистических процессов Москва-2017 Семёнов И.В. 1 , Меньшов И.С. 2 , Немцев М.Ю. 1 Математическое моделирование осесимметричных внутрибаллистических процессов Описаны математическая модель и численный метод для исследования внутрибаллистического процесса в двумерной осесимметричной постановке. Газопороховая смесь моделируется двухфазной неравновесной гетерогенной средой, состоящей из многокомпонентной газовой фазы продуктов горения и полидисперсной конденсированной фазы элементов заряда. Предложен численный метод Годуновского типа для решения неконсервативной системы уравнений Эйлера. Для расчета перемещения метаемого тела используется метод свободной границы для системы уравнений двухфазной гидродинамики. Представлены результаты исследования волнового внутрибаллистического процесса при горении модульного заряда. Ключевые слова: модель двухфазной неравновесной гетерогенной смеси, внутренняя баллистика, горение модульных метательных зарядов Ilya Vitalievich Semenov, Igor Stanislavovich Menshov, Maksim Yurievich Nemtsev Mathematical modeling of the axisymmetric internal ballistics processes Mathematical model and numerical method for investigating the internal ballistics process in a two-dimensional axisymmetric formulation are described. The gas-powder mixture is modeled by a two-phase nonequilibrium heterogeneous medium consisting of a multicomponent gas phase of the combustion products and a polydisperse condensed phase of the charge elements. A numerical method of the Godunov's type is proposed for solving the non-conservative system of Euler equations. To calculate the displacement of the body being thrown, the free boundary method is used for the system of equations of two-phase hydrodynamics. The results of an investigation of the wave interior ballistics process during the combustion of a modular charge are presented.
Uploads
Papers by Igor Menshov