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Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This pa-per verifies the accuracy of an adaptive mesh refinement method numerically using 2-D steady incompressible lid-driven flows and coarser meshes. The accuracy is shown by verifying tha...
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... consider the refined meshes for 2-D lid-driven cavity flows for different mesh sizes and Reynolds number Re = 1000 and 2500, respectively. Because the benchmarks for horizontal velocity ( u ) profiles at x = 0 . 5 and vertical velocity ( v ) profiles at y = 0 . 5 are available, we show the accuracy of the numerical velocity fields by comparing the corresponding profiles obtained from the numerical velocity fields with the corresponding benchmarks. We also show the streamlines of V l generated by Matlab built-in function streamlines , and refined meshes. A grid is called a refined grid if a cross is drawn inside. One of the possible comparisons is the adaptive mesh refinement which refines everywhere that solution gradients are large (Henderson [ 8], 293–299). The refinement criteria enforce everywhere in the mesh, where is the L 2 norm, 1 is the H norm, is the discretization tolerance, u h is finite-dimensional approximation for u , and k in ∇ u ( k ) is the number of subdomains. Fig. 1 (Fig. 5.7 of [8]) shows the refined meshes (left) and vorticity fields ...
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Lid-driven cavity flows have been widely investigated and accurate results
have been achieved as benchmarks for testing the accuracy of computational methods.
This paper investigates sensitivity of a mesh refinement method against the accuracy of
numerical solutions of the 2-D steady incompressible lid-driven flow from a collocated
finite volume me...
Citations
... The accuracy of the mesh refinement method using two-dimensional liddriven cavity flow and a different finite volume method has been established using coarser meshes (65×65 for Re = 1000 and 85×85 for Re = 2500) [21]. It shows that mesh refinement is necessary if we want the relative error of the centre coordinates of tertiary vortices less than 40%. ...
Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper verifies the accuracy of a mesh refinement method numerically using two-dimensional steady incompressible lid-driven flows and finer meshes. The accuracy is shown by comparing the coordinates of centres of vortices located by the mesh refinement method with the corresponding benchmark results. The accuracy verification shows that the mesh refinement method provides refined meshes that all centres of vortices are contained in refined grids based on the numerical solutions of Navier-Stokes equations solved by finite volume method except for one case. The well known SIMPLE algorithm is employed for pressure–velocity coupling. The accuracy of the numerical solutions is shown by comparing the profiles of horizontal and vertical components of velocity fields with the corresponding components of the benchmarks and also streamlines. The mesh refinement method verified in this paper can be applied to find the accurate numerical solutions of any mathematical models containing continuity equations for incompressible fluid or steady state fluid flows or heat transfer.
... The sensitivity analysis of the 2D adaptive mesh refinement for achieving the same above results for the numerical velocity fields obtained by solving mathematical models numerically is considered using 2D lid-driven cavity flows (Li & Lal [16]). The accuracy of the 2D adaptive mesh refinement method is investigated using coarse meshes [17]. ...
... This paper establishes the accuracy of the 2D mesh refinement method using 2D liddriven cavity flows, a different finite volume method from the one used for sensitivity analysis [16] and finer meshes than those used before [17]. A comparison of the accuracy between the second order colocated finite volume method (GSFV) with a splitting method for time discretization [7] and a finite volume method with SIMPLE algorithm [8] has been done Zhenquan Li [15]. ...
