On Applying of Generalized Computational Experiment to Numerical Methods Verification

Alekseev, A. K.; Bondarev, A. E.; Галактионов, В. А.; Kuvshinnikov, Artem E.; Shapiro, L. Z.

doi:10.51130/graphicon-2020-2-3-19

Cited by 10 publications

(9 citation statements)

References 31 publications

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“…Approximating the required surface by a polynomial of the second order using the least squares method, we obtain the following values for the coefficients A = 0.0007426759754917806 B = 0.0005021159520976077 C = 0.00020442857142857106 D = -0.000012584191705984598 E = -0.0000167566591422123 F = 0.0038062569399619252 For a more general comparative assessment, we will calculate the Error Index (EI), similarly to that proposed in [33]. According to [33], the Error Index (EI) is an average value for each error surface. The results for each solver in the L2 norm in accordance with Figure 9 are presented in Table 1.…”

Section: Analysis and Visualization Of Resultsmentioning

confidence: 99%

Analysis and Visualization of the Computational Experiments Results on the Comparative Assessment of OpenFOAM Solvers Accuracy for a Rarefaction Wave Problem

Bondarev¹,

Kuvshinnikov²

2021

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The article is devoted to the analysis and visualization of the generalized computational experiment results on the comparative analysis of the accuracy for a group of open software package OpenFOAM solvers. The basic problem here is the classical problem of the rarefaction wave formation in a flow. This problem has an exact solution which we use as etalon. The generalized computational experiment makes it possible to carry out parametric studies in a grid partition of the region in the space of defining parameters. The construction of a generalized computational experiment is based on the synthesis of mathematical modeling, parallel technologies and visual analytics. As a rule, the results obtained in such an experiment are multidimensional data, on the basis of which the objective functional is constructed, which is the main object of interest of the researcher. In this case, the defining parameters are the input stream Mach number and the flow deflection angle. The deviation from the exact solution calculated in the L1 and L2 norms is considered in the role of the objective functional. For each solver, a parametric problem is solved by varying the Mach number and flow deflection angle. The results obtained represent the dependence of the objective functional on the defining parameters for each solver. The results are presented in visual form as surfaces and in analytical form as polynomials.

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Section: Analysis and Visualization Of Resultsmentioning

confidence: 99%

Analysis and Visualization of the Computational Experiments Results on the Comparative Assessment of OpenFOAM Solvers Accuracy for a Rarefaction Wave Problem

Bondarev¹,

Kuvshinnikov²

2021

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“…Let the centers of the particles satisfy the ODE system (5). We solve the differential part of the system numerically using the explicit Euler scheme:…”

Section: The Basis Of Discontinuous Particle Methodsmentioning

confidence: 99%

“…In addition, particle methods have a constructive inclination to parallelization, economical from the point of view of multidimensionality, ideologically organic to hierarchical transitions between micro-macro models of the considered phenomena. It is worth noting that the problems of evaluating the accuracy of numerical methods on discontinuities currently are very relevant [4,5].…”

Section: Introductionmentioning

confidence: 99%

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

Богомолов¹,

Kuvshinnikov²

2021

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The paper considers a new variant of the discontinuous particle method. The main feature of the new variant is minimal smearing of discontinuities, due to the new criterion of rearrangement of particles. In contrast to the previously used variant with the analysis of overlaps of particles, which required an assumption about their shape, we use the key characteristic of particles, namely, their mass. The assumption is made that in nonlinear elastic transport not only the masses of the particles are conserved, but also the mass located between the centers of these particles. This requirement leads to the fact that a change of distance between particles in the process of their shear and conservation of mass in the space between them, lead to a change of density of one of the particles. The new version applies to solving the one-dimensional and two-dimensional quasi-linear transport equation problem. Visualization is used to monitor the numerical solution, showing that the shock velocity is calculated correctly, and the shock itself is smeared on one particle.

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“…The system was tested on the real results of a generalized computational experiment on the comparative assessment of the accuracy of three solvers (Fig. 3-5) of the open software package OpenFOAM on the problem of supersonic flow around a cone at an angle of attack [20].…”

Section: Key Features and New Options Of The Multi-view Stereomaker 20 Software Packagementioning

confidence: 99%

Expansion of the Functions of the Multi-View Stereomaker Software for Automatic Construction of Complex Stereo Images

Андреев¹,

Bondareva²,

Bondarev³

2021

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This paper presents the second version of the Multi-view StereoMaker 2.0 software package, which allows one to automatically generate complex stereo images according to userspecified parameters. Complex stereo images include both the main object and accompanying inscriptions, formulas and designations. The software package is designed to use the multiview technology on an autostereoscopic monitor and works with arbitrary 3D objects, presenting the results of solving mathematical modeling problems in the form of a stereo image.An autostereoscopic monitor allows one to view stereo images without glasses, while providing quality that rivals classic 3D projection stereo systems.The description of the main changes and new features of the second version of the developed system is given. The results of the operation of the Multi-view StereoMaker software complex on real problems are presented.

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On Applying of Generalized Computational Experiment to Numerical Methods Verification

Cited by 10 publications

References 31 publications

Analysis and Visualization of the Computational Experiments Results on the Comparative Assessment of OpenFOAM Solvers Accuracy for a Rarefaction Wave Problem

Analysis and Visualization of the Computational Experiments Results on the Comparative Assessment of OpenFOAM Solvers Accuracy for a Rarefaction Wave Problem

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

Expansion of the Functions of the Multi-View Stereomaker Software for Automatic Construction of Complex Stereo Images

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