Boris Korneev - Academia.edu (original) (raw)

Papers by Boris Korneev

Mathematical Models and Computer Simulations, Nov 1, 2021

Journal of Computational and Applied Mathematics, May 1, 2023

Journal of Physics: Conference Series, 2021

Numerical simulation is widely used as a main way of researching the processes described by the s... more Numerical simulation is widely used as a main way of researching the processes described by the systems of partial differential equations in the divergence form, like fluid dynamics, traffic flow, wave propagation. To obtain desired accuracy and resolution, the high-order numerical methods are used. In this paper we consider the Runge-Kutta (RK) time discretization, when the space discretization can be high-order finite volume method, discontinuous Galerkin method or others. Presence of discrete analogue of conservation is considered to be very important for such methods as it corresponds to the essential feature of simulated process, becoming especially vital at the discontinuous solutions. The adaptive mesh refinement (AMR) techniques are used to get the numerical solution with more resolution where needed. For the explicit numerical scheme obeying the Courant-Friedrichs-Lewy (CFL) condition, the bigger time integration step can be chosen for the coarser cells. The problem is how ...

2022 6th High Performance Computing and Cluster Technologies Conference (HPCCT)

Математическое моделирование, 2021

Работа посвящена численному исследованию конечно-объемной схемы с потоком HLLEM для решения уравн... more Работа посвящена численному исследованию конечно-объемной схемы с потоком HLLEM для решения уравнений из семейства моделей Баера-Нунциато. Рассматривается три варианта модели, отличающихся степенью «неравновесности». Приводится краткое описание моделей и их отличия. Для аппроксимации уравнений неравновесных моделей с жесткими правыми частями, описывающими процесс механической и термодинамической релаксации, используется метод расщепления по физическим процессам. Пространственные аппроксимации строятся методом конечных объемов 1-го и 2-го порядка (TVD). В качестве численного потока используется поток HLLEM, для которого предложен простой алгоритм определения параметра метода, гарантирующего физичность решения. Особенностью работы является то, что все три рассмотренные модели применены для анализа фактически одной и той же физической постановки.

CIMNE, 2019

We present the results of a 3D modeling of the laser powder bed fusion process on the mesoscale l... more We present the results of a 3D modeling of the laser powder bed fusion process on the mesoscale level with an advanced multiphysical numerical tool. High-performance simulation allowed to conduct a vast parametric study. Thus, the model has been extensively verified against experimental results in a large parameter range, and, further, it has been used to construct detailed process maps in the range not covered by the available experimental data. The analysis of the results that were obtained in the model along with the data in the published research allowed to propose the quantitative criteria for determining the behavior of the track formation. The key phenomena that affect this behavior have been studied. We conclude that the productivity limit that arises with the proportional increase in scanning speed and laser beam power is caused by the spatter ejection. The sensitivity analysis shows that the transition to the spattering regime is caused by the overheating of the meltpool surface layer, and, consequently, the development of the surface instability. The instability development is assumed to be due to the fact that the recoil pressure becomes much higher in comparison with the surface tension.

2019 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), 2019

The algorithm of implementation for the computational fluid dynamics solver based on the Runge Ku... more The algorithm of implementation for the computational fluid dynamics solver based on the Runge Kutta discontinuous Galerkin numerical method and the locally-recursive non-locally asynchronous algorithm ‘DiamondTorre’ is described. The essence of the algorithm is the space-time asynchronous bypass of the numerical domain based on the stencil dependency graph of the numerical scheme. Performance tests of the created implementation are carried out on several GPUs, demonstrating the speed of the solver to be more than 108 cells per second at a single GPU. The software can be applied to numerically solve fluid shock-body interaction problems.

Communications in Computer and Information Science, 2020

Additive Manufacturing, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Keldysh Institute Preprints, 2018

1 MIPT, 2 KIAM RAS Simulating three-dimensional unsteady viscous compressible flow on GPU using t... more 1 MIPT, 2 KIAM RAS Simulating three-dimensional unsteady viscous compressible flow on GPU using the DiamondTorre algorithm In this paper the approach to simulation of unsteady fluid dynamic problems in terms of the Navier-Stokes system of equations is considered. The numerical scheme is built using the Runge-Kutta discontinuous Galerkin method, approximating the viscous terms with the local discontinuous Galerkin method. A modification of the DiamondTorre algorithm is developped for the geterogeneous implementation of the scheme. The solver based on this algorithm is included into the DTGV software for solving three-dimensional fluid dynamic problems, the results of its validation and performance tests are given. An example of solving the problem of flow past a sphere in three-dimensional setting is presented.

Keldysh Institute Preprints, 2019

On the conservativity of the Particles-on-Demand method for the solution of the Discrete Boltzman... more On the conservativity of the Particles-on-Demand method for the solution of the Discrete Boltzmann Equation It is well known that the standard Lattice-Boltzmann method (LBM) is applicable in the range of small flow velocities and under the isothermal conditions. The novel Particle-on-demand method [1] allows to numerically solve the discrete Boltzmann equation for high Mach numbers. We validate its capabilities with our implementation on the problems with shock waves. In comparison with the standard Lattice Boltzmann Method, the collision step is simple, but the streaming step is implicit, non-conservative and excessively computationally heavy. We propose a way that in specific cases improves the method by making the streaming step explicit and conservative. The results are validated by examining the total mass, momentum and energy change in the problem of shock formation due to the sound wave distortion. The scheme also performs well in both 1D and 3D test Sod problems.

Computational Mathematics and Mathematical Physics, 2016

In this paper we present the Runge-Kutta discontinuous Galerkin method (RKDG method) for the nume... more In this paper we present the Runge-Kutta discontinuous Galerkin method (RKDG method) for the numerical solution of the Euler equations of gas dynamics. The method is being tested on a series of Riemann problems in the one-dimensional case. For the implementation of the method in the three-dimensional case, a DiamondTorre algorithm is proposed. It belongs to the class of the locally recursive non-locally asynchronous algorithms (LRnLA). With the help of this algorithm a significant increase of speed of calculations is achieved. As an example of the three-dimensional computing, a problem of the interaction of a bubble with a shock wave is considered.

Procedia Computer Science, 2015

In this paper the solver based upon the RKDG method for solving three-dimensional Euler equations... more In this paper the solver based upon the RKDG method for solving three-dimensional Euler equations of gas dynamics is considered. For the numerical scheme the GPU implementation algorithm called DiamondTorre is used, which helps to improve the performance speed of calculations. The problem of the interaction of a spherical bubble with a planar shock wave is considered in the three-dimensional setting. The obtained calculations are in agreement with the known results of experiments and numerical simulations. The calculation results are obtained with the use of the PC.

Journal of Physics: Conference Series, 2016

Interaction between a shock wave and an inhomogeneity in fluid has complicated behavior, includin... more Interaction between a shock wave and an inhomogeneity in fluid has complicated behavior, including vortex and turbulence generating, mixing, shock wave scattering and reflection. In the present paper we deal with the numerical simulation of the considered process. The Euler equations of unsteady inviscid compressible three-dimensional flow are used into the four-equation model of multicomponent flow. These equations are discretized using the RKDG numerical method. It is implemented with the help of the DiamondTorre algorithm, so the effective GPGPU solver is obtained having outstanding computing properties. With its use we carry out several sets of numerical experiments of shock-bubble interaction problem. The bubble deformation and mixture formation is observed.

Fluid Dynamics Research, 2016

A set of numerical experiments on the interaction between a planar shock wave and a spherical bub... more A set of numerical experiments on the interaction between a planar shock wave and a spherical bubble with a slightly perturbed surface is considered. Spectral analysis of the instability growth is carried out and three-dimensional Euler equations of fluid dynamics are chosen as the mathematical model for the process. The equations are solved via the Runge–Kutta discontinuous Galerkin method and the special DiamondTorre algorithm for multi-GPU implementation is used.