Published 4 issues per year
ISSN Print: 1065-3090
ISSN Online: 1940-4336
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AN ADAPTIVE THREE-DIMENSIONAL MESH REFINEMENT METHOD BASED ON THE LAW OF MASS CONSERVATION
ABSTRACT
Mesh generation is one of key issues in Computational Fluid Dynamics. This paper presents an adaptive three-dimensional mesh refinement method based on the law of mass conservation. The method can be applied to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. Users can choose how many refinements they want to perform on the initial mesh. The more the number of refinements, the less the error of calculations is. The refined meshes can identify the accurate locations of asymptotes, the points at which one, two, or all components of velocity fields are equal to zero, and draw accurate closed streamlines if the number of refinements is big enough and the initial mesh is fine enough. We show three examples that demonstrate the claims.
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Lal Rajnesh, Li Zhenquan, Sensitivity analysis of a mesh refinement method using the numerical solutions of 2D lid-driven cavity flow, Journal of Mathematical Chemistry, 53, 3, 2015. Crossref
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Li Zhenquan, Wood Robert, Accuracy analysis of an adaptive mesh refinement method using benchmarks of 2-D steady incompressible lid-driven cavity flows and coarser meshes, Journal of Computational and Applied Mathematics, 275, 2015. Crossref
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Li Zhenquan, Accuracy analysis of a mesh refinement method using benchmarks of 2-D lid-driven cavity flows and finer meshes, Journal of Mathematical Chemistry, 52, 4, 2014. Crossref
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Li Zhenquan, Lal Rajnesh, An Application of a Mesh Refinement Method Based on the Law of Mass Conservation, 2010 International Conference on Computational and Information Sciences, 2010. Crossref
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Crowhurst P., Zhenquan Li , Numerical Solutions of One-Dimensional Shallow Water Equations, 2013 UKSim 15th International Conference on Computer Modelling and Simulation, 2013. Crossref
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Li Zhenquan, Crowhurst Peter, Wood Robert, Error Driven Node Placement as Applied to One Dimensional Shallow Water Equations, 2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim), 2015. Crossref
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Li Zhenquan, Wood Robert, Accuracy verification of a 2D adaptive mesh refinement method for incompressible or steady flow, Journal of Computational and Applied Mathematics, 318, 2017. Crossref
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Li Zhenquan, Li Miao, Accuracy Verification of a 2D Adaptive Mesh Refinement Method Using Backward-Facing Step Flow of Low Reynolds Numbers, International Journal of Computational Methods, 18, 03, 2021. Crossref