{"title":"针对小长度尺度上参数对比较大的断裂介质中的流动和传输问题的空间和时间方案对比研究","authors":"Wansheng Gao, Insa Neuweiler, Thomas Wick","doi":"10.1007/s10596-024-10293-y","DOIUrl":null,"url":null,"abstract":"<p>In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.</p>","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":"150 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales\",\"authors\":\"Wansheng Gao, Insa Neuweiler, Thomas Wick\",\"doi\":\"10.1007/s10596-024-10293-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.</p>\",\"PeriodicalId\":10662,\"journal\":{\"name\":\"Computational Geosciences\",\"volume\":\"150 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Geosciences\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.1007/s10596-024-10293-y\",\"RegionNum\":3,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Geosciences","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1007/s10596-024-10293-y","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales
In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.
期刊介绍:
Computational Geosciences publishes high quality papers on mathematical modeling, simulation, numerical analysis, and other computational aspects of the geosciences. In particular the journal is focused on advanced numerical methods for the simulation of subsurface flow and transport, and associated aspects such as discretization, gridding, upscaling, optimization, data assimilation, uncertainty assessment, and high performance parallel and grid computing.
Papers treating similar topics but with applications to other fields in the geosciences, such as geomechanics, geophysics, oceanography, or meteorology, will also be considered.
The journal provides a platform for interaction and multidisciplinary collaboration among diverse scientific groups, from both academia and industry, which share an interest in developing mathematical models and efficient algorithms for solving them, such as mathematicians, engineers, chemists, physicists, and geoscientists.