Geodesic
On one method of calculating moving boundaries in Euler coordinates
Journal of computational and engineering mathematics, Tome 6 (2019) no. 4, pp. 44-56.

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The paper presents a method for calculating a moving boundary in Euler coordinates as an application to studies of gas flows in areas with an impermeable wall. The method is based on a combination of the Eulerian grid and one Lagrangian border cell formed by the combination of two cells adjacent directly to the moving border. Reconstruction of the entire computational domain is not required. This fact has a significant impact on the computational performance. We describe the algorithm for combination of cells, present the calculation of thermodynamic parameters, and justify the expression for the internal energy of the combined interval. The method was verified using an analytical solution to the problem of a converging shock wave in a vessel with an impermeable wall. Finally, we compare the entropy functions of the analytical and numerical solutions.
Keywords: numerical method, moving boundary, Euler coordinates, method of large particles, converging shock wave. 
@article{JCEM_2019_6_4_a3,
     author = {E. S. Shestakovskaya and Ya. E. Starikov},
     title = {On one method of calculating moving boundaries in {Euler} coordinates},
     journal = {Journal of computational and engineering mathematics},
     pages = {44--56},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2019_6_4_a3/}
}
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E. S. Shestakovskaya; Ya. E. Starikov. On one method of calculating moving boundaries in Euler coordinates. Journal of computational and engineering mathematics, Tome 6 (2019) no. 4, pp. 44-56. http://geodesic.mathdoc.fr/item/JCEM_2019_6_4_a3/