The lid-driven square cavity flow: numerical solution with a 1024 x 1024 grid
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The problem of flow inside a square cavity whose lid has constant velocity is solved by the Navier-Stokes equations using the finite volume method with numerical approximations of second-order accuracy and multiple Richardson extrapolations.Abstract:
The problem of flow inside a square cavity whose lid has constant velocity is solved This problem is modeled by the Navier-Stokes equations The numerical model is based on the finite volume method with numerical approximations of second-order accuracy and multiple Richardson extrapolations (MRE) The iterative process was repeated until the machine round-off error achievement This work presents results for 42 variables of interest, and their discretization errors estimates, on the 1024 x 1024 nodes grid and the following Reynolds numbers: 001, 10, 100, 400 and 1000 These results are compared with sixteen sources in literature The numerical solutions of this work are the most accurate obtained for this problem to date The use of multiple Richardson extrapolations reduces the discretization error significantlyread more
Citations
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Journal ArticleDOI
Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach
TL;DR: In this article, the optimum conditions of the mixed convection heat transfer in a wavy surface square cavity filled with Cu-water nanofluid by utilizing the Taguchi method is presented.
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A New Theoretical Approach of Wall Transpiration in the Cavity Flow of the Ferrofluids
TL;DR: It is found that the secondary vortices residing on the lower wall of the cavity are dissolved by the implementation of the suction/injection chamber, and their character is dependent on the rate of permeability.
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Distributed learning machines for solving forward and inverse problems in partial differential equations
TL;DR: It is shown that ideas of linearization and time-marching allow DPIELM to be able to solve nonlinear PDEs to some extent and that DPINNs have potential advantages over existing PINNs to solve the inverse problems in heterogeneous media.
Journal ArticleDOI
Highly accurate numerical solutions with repeated Richardson extrapolation for 2D laplace equation
Carlos Henrique Marchi,Leandro Alberto Novak,Cosmo Damião Santiago,Ana Paula da Silveira Vargas +3 more
TL;DR: A theoretical basis is presented for the repeated Richardson extrapolation (RRE) to reduce and estimate the discretization error of numerical solutions for heat conduction and to obtain a given value error, much less CPU time and RAM memory are required for the solution with RRE than without it.
Book ChapterDOI
FVCA8 Benchmark for the Stokes and Navier–Stokes Equations with the TrioCFD Code—Benchmark Session
TL;DR: The study of convergence orders of several numerical methods implemented in the TrioCFD code dedicated to the simulation of turbulent flows and heat transfer in nuclear engineering applications and the well-known lid-driven cavity flow case is studied.
References
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Computational methods for fluid dynamics
Joel H. Ferziger,Milovan Perić +1 more
TL;DR: This text develops and applies the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice, including advanced techniques in computational fluid dynamics.
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High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
U Ghia,K.N Ghia,C. T. Shin +2 more
TL;DR: The vorticity-stream function formulation of the two-dimensional incompressible NavierStokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions.
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Advanced Engineering Mathematics
TL;DR: This book discusses ODEs, Partial Differential Equations, Fourier Series, Integrals, and Transforms, and Numerics for ODE's and PDE's, as well as numerical analysis and potential theory, and more.
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Enhancements of the simple method for predicting incompressible fluid flows
J. P. Van Doormaal,G. D. Raithby +1 more
TL;DR: The performances of SIMPLE, SIMPLER, and SIMPLEC are compared for two recirculating flow problems and several modifications to the method are shown which both simplify its implementation and reduce solution costs.
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Natural convection of air in a square cavity: A bench mark numerical solution
TL;DR: In this paper, the authors used mesh refnement and extrapolation to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls.
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