E. A. Veselova, Yu. N. Deryugin, D. K. Zelensky

Russian Federal Nuclear Center – All-Russian Scientific Research Institute of Experimental Physics (RFNC-VNIIEF (Sarov, Russian Federation)

Abstract. The paper presents a methodology for numerical solution of two-dimensional gas dynamics problems using geometrically adaptive moving unstructured meshes. Geometric adaptation agrees well with an approach based on highlighting of shock waves and contact discontinuities as solution features. Displacement of internal mesh nodes is found via displacement of boundary nodes. Velocities of discontinuities and other their parameters are determined using Riemann’s problem on a discontinuity breakup. Discretization of initial equations in an integral form is provided. Accuracy increase for the calculation is achieved by determination of pre-breakup flow parameters and by linear or quadratic reconstruction of the flow. In spherically-symmetric problems the algorithm of additional turn of pre-breakup flow velocity is applied. The method is tried out on test problems and applied to modelling of a shock wave that is induced by a spherical charge explosion and propagates over a large distance. Basing on calculation results dependencies of excessive pressure on a distance covered by the wave are obtained. Numerical investigation of the flow structure behind a wave is provided for large distances covered by this wave. Also numerical modelling demonstrated that the wave has N-form that is consequent with earlier results.

Key Words: gas dynamics, shock wave, unstructured mesh, Godunov method, LOGOS-WAVE

For citation: E. A. Veselova, Yu. N. Deryugin, D. K. Zelensky. Numerical modeling of air shock wave propagation on a moving unstructured mesh. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:1(2026), 96–116. DOI: https://doi.org/10.15507/2079-6900.28.202601.96-116

Information about the authors:

Elena A. Veselova, Senior Researcher, RFNC-VNIIEF (37 Mira Ave, Sarov, Nizhny Novgorod region, 607188, Russia), ORCID: https://orcid.org/0000-0002-9042-3415, sarov333@gmail.com

Yuriy N. Deryugin, D. Sci. (Phys. and Math.), Chief Researcher, RFNC-VNIIEF (37 Mira Ave, Sarov, Nizhny Novgorod region, 607188, Russia), ORCID: https://orcid.org/0000-0002- 3955-775X, dyn1947@yandex.ru

Dmitry K. Zelensky, Head of the Laboratory, RFNC-VNIIEF (37 Mira Ave, Sarov, Nizhny Novgorod region, 607188, Russia), zdk@vniief.ru