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

Abstract

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.

Visualization of Calculations of the Discontinuous Particle Method in Problems with Viscosity

“…The pressure difference on the left and right sides of a particle leads to changes in its momentum and energy, increasing the volume of the respective particles. Similarly to [8], we arrive at the following computational formulas:…”

“…The study of applying the discontinuous particle method to viscous problems was conducted as part of a comprehensive research effort comparing the relative accuracy of numerical methods on benchmark solutions. This research was previously carried out for inviscid gas dynamics problems with benchmark solutions presented in [6][7][8]. Currently, research is ongoing to comparatively assess the accuracy of numerical methods for viscous problems using benchmark solutions.…”

Comparative Evaluation of the Accuracy of Numerical Methods on Reference Solutions

“…Additionally, problems involving the formation of oblique shock waves when a supersonic flow impinges on a plate at a certain angle were examined [8,9]. In these cases, the freestream velocity and the angle of incidence of the flow on the plate were the varied parameters.…”

An extension of the all-Mach number pressure-based solution framework for numerical modelling of two-phase flows with interface

“…For the single phase modelling including multicomponent gases, a pressure-based numerical tool employing the hybrid approximation of convective fluxes [9,10] was developed earlier. The solver has been validated against different physical conditions [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and for the wide range of Mach numbers. The next step for the framework development was the adaptation for simulation of high-speed multicomponent real-gas flows [27,28] in context of consideration of the phase separation phenomenon.…”