SUPERCONVERGENCE OF MIXED COVOLUME METHOD ON QUADRILATERAL GRIDS FOR ELLIPTIC PROBLEMS

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h^2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h^2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L^2 norm.Numerical experiments illustrating the theoretical results are provided.

An open-source web service for creating quadrilateral grids based on the rHEALPix Discrete Global Grid System

The foundation of modern Digital Earth frameworks is the Discrete Global Grid System(DGGS).To standardize the DGGS model,the Open Geospatial Consortium(OGC)recently created the DGGS Abstract Specification,which also aims to increase usability and interoperability between DGGSs.To support these demands and aid future research,open implementations are necessary.However,several OGC conformant DGGSs are not available for researchers to use.This has motivated us to develop an open-source web service that allows users to create quadrilateral grids based on the rHEALPix DGGS.In this paper,we describe the implementation of the web service,including issues and limitations,and demonstrate how discrete global grids and regional grids can be created.Lastly,we present examples that show how vector data sets can be modeled and integrated at different levels of resolution–a key benefit of the DGGS model.

An automatic isotropic/anisotropic hybrid grid generation technique for viscous flow simulations based on an artificial neural network

Based on the author’s previous research, a novel hybrid grid generation technique is developed by introducing an Artificial Neural Network(ANN) approach for realistic viscous flow simulations. An initial hybrid grid over a typical geometry with anisotropic quadrilaterals in the boundary layer and isotropic triangles in the off-body region is generated by the classical mesh generation method to train two ANNs on how to predict the advancing direction of the new point and to control the grid size. After inputting the initial discretized fronts, the ANN-based Advancing Layer Method(ALM) is adopted to generate the anisotropic quadrilaterals in boundary layers. When the high aspect ratio of the anisotropic grid reaches a specified value, the ANN-based Advancing Front Method(AFM) is adopted to generate isotropic triangles in the off-body computational domain.The initial isotropic triangles are smoothed to further improve the grid quality. Three typical cases are tested and compared with experimental data to validate the effectiveness of grids generated by the ANN-based hybrid grid generation method. The experimental results show that the two ANNs can predict the advancing direction and the grid size very well, and improve the adaptability of the isotropic/anisotropic hybrid grid generation for viscous flow simulations.