Solving Hydrodynamic Problems Based on a Modified Upwind Leapfrog Scheme in Areas with Complex Geometry

Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova () and Elena Rahimbaeva
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Alexander Sukhinov: Department of Mathematics and Computer Science, Don State Technical University, 344000 Rostov-on-Don, Russia
Alexander Chistyakov: Department of Mathematics and Computer Science, Don State Technical University, 344000 Rostov-on-Don, Russia
Inna Kuznetsova: Department of Mathematics and Computer Science, Don State Technical University, 344000 Rostov-on-Don, Russia
Yulia Belova: Department of Mathematics and Computer Science, Don State Technical University, 344000 Rostov-on-Don, Russia
Elena Rahimbaeva: Department of Mathematics and Computer Science, Don State Technical University, 344000 Rostov-on-Don, Russia

Mathematics, 2022, vol. 10, issue 18, 1-18

Abstract: In recent years, the number of adverse and dangerous natural and anthropogenic phenomena has increased in coastal zones around the world. The development of mathematical modeling methods allows us to increase the accuracy of the study of hydrodynamic processes and the prediction of extreme events. This article discusses the application of the modified Upwind Leapfrog scheme to the numerical solution of hydrodynamics and convection–diffusion problems. To improve the accuracy of solving the tasks in the field of complex shapes, the method of filling cells is used. Numerical experiments have been carried out to simulate the flow of a viscous liquid and the transfer of substances using a linear combination of Upwind and Standard Leapfrog difference schemes. It is shown that the application of the methods proposed in the article allows us to reduce the approximation error in comparison with standard schemes in the case of large grid numbers of Péclet and to increase the smoothness of the solution accuracy at the boundary. The soil dumping and suspended matter propagation problems are solved using the developed schemes.

Keywords: Upwind Leapfrog scheme; Standard Leapfrog scheme; large grid Péclet numbers; hydrodynamics model; the problem of soil dumping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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