Development of algorithms for constructing two-dimensional optimal boundary-adaptive grids and their software implementation
Open Access
- 18 October 2021
- journal article
- Published by FSFEI HE Don State Technical University in Advanced Engineering Research
- Vol. 21 (3), 222-230
- https://doi.org/10.23947/2687-1653-2021-21-3-222-230
Abstract
Introduction. It is noted that the use of adaptive grids in calculations makes it possible to improve the accuracy and efficiency of computational algorithms without increasing the number of nodes. This approach is especially efficient when calculating nonstationary problems. The objective of this study is the development, construction and software implementation of methods for constructing computational two-dimensional optimal boundary-adaptive grids for complex configuration regions while maintaining the specified features of the shape and boundary of the region. The application of such methods contributes to improving the accuracy, efficiency, and cost-effectiveness of computational algorithms. Materials and Methods. The problem of automatic construction of an optimal boundary-adaptive grid in a simply connected region of arbitrary geometry, topologically equivalent to a rectangle, is considered. A solution is obtained for the minimum set of input information: the boundary of the region in the physical plane and the number of points on it are given. The creation of an algorithm and a mesh generation program is based on a model of particle dynamics. This provides determining the trajectories of individual particles and studying the dynamics of their pair interaction in the system under consideration. The interior and border nodes of the grid are separated through using the mask tool, and this makes it possible to determine the speed of movement of nodes, taking into account the specifics of the problem being solved. Results. The developed methods for constructing an optimal boundary-adaptive grid of a complex geometry region provides solving the problem on automatic grid construction in two-dimensional regions of any configuration. To evaluate the results of the algorithm research, a test problem was solved, and the solution stages were visualized. The computational domain of the test problem and the operation of the function for calculating the speed of movement of interior nodes are shown in the form of figures. Visualization confirms the advantage of this meshing method, which separates the border and interior nodes. Discussion and Conclusions. The theoretical and numerical studies results are important both for the investigation of the grids qualitative properties and for the computational grid methods that provide solving numerical modeling problems efficiently and with high accuracy.Keywords
This publication has 10 references indexed in Scilit:
- Correction to: Tidal Asymmetry in Ocean-Boundary Flux and In-Estuary Trapping of Suspended Sediment Following Watershed Storms: San Francisco Estuary, California, USAEstuaries and Coasts, 2021
- Development and correctness analysis of the mathematical model of transport and suspension sedimentation depending on bottom relief variationAdvanced Engineering Research, 2018
- Well-posedness analysis and numerical implementation of a linearized two-dimensional bottom sediment transport problemComputational Mathematics and Mathematical Physics, 2017
- Sufficient conditions for convergence of positive solutions to linearized two-dimensional sediment transport problemВестник Донского государственного технического университета, 2017
- Predictive modeling in sediment transportation across multiple spatial scales in the Jialing River Basin of ChinaInternational Journal of Sediment Research, 2015
- Modelled transport of benthic marine microplastic pollution in the Nazaré CanyonBiogeosciences (online), 2013
- Sediment transport in the San Francisco Bay Coastal System: An overviewMarine Geology, 2013
- Coastal hydrodynamics in a windy lagoonComputers & Fluids, 2013
- Some aspects of adaptive grid technology related to boundary and interior layersJournal of Computational and Applied Mathematics, 2004
- Nested Grid Iteration for Incompressible Viscous Flow and TransportInternational Journal of Computational Fluid Dynamics, 2003