About one version of the nodal method of characteristics

Surov V.S.
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A variant of the inverse method of characteristics (IMH) is presented, in whose algorithm an additional fractional time step is introduced, which makes it possible to increase the accuracy of calculations due to a more accurate approximation of the characteristics. The calculation formulas of the modified method for the equations of the one-velocity model of a gas-liquid mixture are given, with the help of which one-dimensional and also flat test problems with self-similar solutions are calculated. When solving multidimensional problems, the original system of equations is split into a number of one-dimensional subsystems, for the calculation of which the inverse method of characteristics with a fractional time step is used. Using the proposed method, the following were calculated: the one-dimensional problem of the decay of an arbitrary discontinuity in a dispersed medium; a twodimensional problem of the interaction of a homogeneous gas-liquid flow with an obstacle with an attached shock wave, as well as a flow with a centered rarefaction wave. The results of numerical calculations of these problems are compared with self-similar solutions and their satisfactory agreement is noted. On the example of the Riemann problem with a shock wave, a comparison is made with a number of conservative, non-conservative, first and higher orders of accuracy schemes, from which, in particular, it follows that the presented calculation method, i. e. MIMC, quite competitive. Despite the fact that the application of MIMC requires many times more time than the original inverse method of characteristics (IMC), calculations can be carried out with an increased time step and, in some cases, more accurate results can be obtained. It is noted that the method with a fractional time step has advantages over the IMC in cases where the characteristics of the system are significantly curvilinear. For this reason, the use of MIMC, for example, for the Euler equations is inappropriate, since for the latter the characteristics within the time step differ little from straight lines.

Keywords: hyperbolic models, reverse characteristic method, multidimensional nodal characteristic method
Citation in English: Surov V.S. About one version of the nodal method of characteristics // Computer Research and Modeling, 2023, vol. 15, no. 1, pp. 29-44
Citation in English: Surov V.S. About one version of the nodal method of characteristics // Computer Research and Modeling, 2023, vol. 15, no. 1, pp. 29-44
DOI: 10.20537/2076-7633-2023-15-1-29-44
URL: http://crm-en.ics.org.ru/journal/article/3287/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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