Aleksyuk A. I., Belikov V. V. Simulation of shallow water flows with shoaling areas and bottom discontinuities // Computational Mathematics and Mathematical Physics. — 2017. — Vol. 57, no. 2. — P. 318–339.
A numerical method based on a second-order accurate Godunov-type scheme is described for solving the shallow water equations on unstructured triangular-quadrilateral meshes. The bottom surface is represented by a piecewise linear approximation with discontinuities, and a new approximate Riemann solver is used to treat the bottom jump. Flows with a dry sloping bottom are computed using a simplified method that admits negative depths and preserves the liquid mass and the equilibrium state. The accuracy and performance of the approach proposed for shallow water flow simulation are illustrated by computing one- and two-dimensional problems.
2018Vavilin V.A., Rytov S.V., Lokshina L.Y. Modelling the specific pathway of CH4 and CO2 formation using carbon isotope fractionation: an example for a boreal mesotrophic fen / Isotopes in Environmental and Health Studies
2018V.A. Vavilin, S.V. Rytov, L.Y. Lokshina. Dynamic isotope equations for 13CH4 and 13CO2 describing methane formation with a focus on the effect of anaerobic respiration in sediments of some tropical lakes / Ecological Modelling, 2018, vol. 386, pages 59-70