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3D DNS of laminar Rayleigh-Bénard convection in a cylinder for incompressible fluid flow 1 1 Introduction 1 2 Physical and mathematical models 4 2.1 Physical model 4 2.2 Mathematical model 4 3 Numerical methods and verification 6 3.1 The improved projection scheme (IPS) 6 3.2 The artificial compressibility method (ACM) 7 3.3 Time discretization and spatial discretization 8 3.3.1 Time discretization 8 3.3.2 Spatial discretization 8 3.4 Grid independence test and code validation 13 4 Results and discussion 16 4.1 Performance comparisons among four syntheses for 2×103≤Ra≤2×104, Pr=1 at Γ=1 16 4.2 Numerical results for 3×103≤Ra≤5×104 at Γ=1 and 3×103≤Ra≤3×104 at Γ=2 17 5 Conclusions and remarks 19 Declaration of Competing Interest 20 Acknowledgments 20 References 20

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UND

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nonfiction