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A study of the behaviour of flow past a square cylinder for Reynolds numbers 10 and 20 is presented. Open source software Navier2d in Matlab is used in this study. The investigation starts from a uniform initial mesh and then refine the initial mesh using a mesh refinement method which was proposed based on both qualitative theory of differential e...
Citations
... The AMR method refines a given mesh based on the numerically computed velocity fields. The efficiency and accuracy of the AMR method has been verified using the accurate locations of singular points, asymptotic lines and closed streamlines [12], and against widely used CFD benchmark experiments including the lid-driven cavity flow [11], the 2D unsteady flow past a square cylinder [14], the backward-facing step flow [17] and 2D flow over a wall-mounted plate [16]. In particular, the AMR method has been shown to be useful for capturing localized flow features such as accurate location of the centre of vortices within the refined cells [11,16]. ...
... The AMR method is robust [11], low-cost [15] and can be applied to any incompressible fluid flow [18]. The previous works, for example, [14,17], considered the accuracy of the 2D AMR method with two refinements and used the finite volume methods. We showed that the twice-refined cells contain the centre of vortices. ...
The study applies a two-dimensional adaptive mesh refinement (AMR) method to estimate the coordinates of the locations of the centre of vortices in steady, incompressible flow around a square cylinder placed within a channel. The AMR method is robust and low cost, and can be applied to any incompressible fluid flow. The considered channel has a blockage ratio of 1/8. The AMR is tested on eight cases, considering flows with different Reynolds numbers (5 ≤ Re ≤ 50), and the estimated coordinates of the location of the centres of vortices are reported. For all test cases, the initial coarse meshes are refined four times, and the results are in good agreement with the literature where a very fine mesh was used. Furthermore, this study shows that the AMR method can capture the location of the centre of vortices within the fourth refined cells, and further confirms an improvement in the estimation with more refinements.
Keywords and phrases: two-dimensional flow over square cylinder, adaptive mesh refinement, centre of vortices.
... This AMR method refines a computational mesh using numerically computed velocity fields. The efficacy and accuracy of this AMR method have been verified through the accurate locations of singular points, asymptotic lines, and closed streamlines [9], as well as through comparisons with established CFD benchmark experiments up to two refinements, including lid-driven cavity flow [10], 2D unsteady flow past a square cylinder [11], backwards-facing step flow [12], and 2D flow over a wall-mounted plate [13]. Furthermore, the AMR method has demonstrated its capability to capture localized flow features, such as identifying accurate locations of the centre of vortices within refined cells [10,13]. ...
The lid-driven cavity flow problem is a well-known test case in fluid dynamics for validating computational fluid dynamics (CFD) algorithms. Despite its geometrical simplicity, the lid driven cavity flow problem exhibits a complex flow regime, mainly due to the vortices formed in the centre and at the corners of the square domain. Consequently, this paper verifies the accuracy of a 2D adaptive mesh refinement (AMR) method in estimating the locations of the centre of vortices for a steady incompressible flow in a 2D lid-driven square cavity. We consider an initial coarse uniform grid mesh with a resolution of 20×20 and 50×50 for Reynolds number Re = 1000 and 2500, respectively and perform ten refinements. Our study reports the location of the centre of vortices obtained for Re = 1000 and 2500. The accuracy of the result is shown by comparing the coordinates of centres of vortices located by the AMR method with the corresponding benchmark results from four different literature.
... The theory which supports the 2D AMR technique has been previously demonstrated by adaptive streamline tracking using the same above accuracy measures and analytical velocity fields [Li (2002)]. Furthermore, the accuracy of Li's 2D AMR method has been verified using several common CFD benchmark experiments, including the lid-driven cavity flow [Lal and Li (2015); Li and Wood (2017)], the 2D unsteady flow past a square cylinder [Li (2017b)], and the backwards-facing step flow [Li and Li (2021)]. The 2D AMR method has also been shown to possess the capability to capture the accurate 2341001-3 Int. ...
Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.
... The mesh refinement technique [13] [14] has previously been verified using the accurate locations of singular points, asymptotic lines, and closed streamlines [16]- [18]. Moreover, the accuracy of the 2D AMR method has also been verified against the commonly used CFD benchmark experiments such as the lid-driven cavity flow [19]- [22], the 2D unsteady flow past a square cylinder [23], and the backwardfacing step flow [24]. Additionally, the AMR proposed by Li [13] [14] has been shown to capture the centre of vortices within the refined cells of once refined meshes and within the twice refined cells after applying the AMR algorithm twice [21] [25]. ...
Meshing plays an important role on the accuracy and convergence of CFD solvers. The accuracy includes quantitative measures such as discretization and truncation errors and qualitative measures such as drawing closed streamline, identifying singular points, asymptotic lines/planes, and (symmetry) axis. The current study builds on previous work by further demonstrating the accuracy of the three-dimensional adaptive mesh refinement method by comparing the accuracy measures between the ones derived from analytical velocity fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is proposed based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The performance of the adaptive mesh refinement method is analysed using three-dimensional analytic velocity fields of four examples. The results provide evidence for the accuracy of the mesh refinement method in identifying the singular points, axes, and asymptote planes of the analytical velocity fields.
... The AMR method proposed by Li [2007;2008] has been verified using the accurate locations of singular points, asymptotic lines, and closed streamlines [Li (2002); Li (2006a); Li (2006b)]. Furthermore, the accuracy of the 2D AMR method has been verified against the widely used CFD benchmark experiments such as the lid-driven cavity flow [Li (2014); Lal and Li (2015); Li and Wood (2017); Li (2017a)], the 2D unsteady flow past a square cylinder [Li (2017b)], and the backward-facing step flow [Li and Li (2021)]. ...
This paper describes the application of an adaptive mesh refinement (AMR) method to estimate centers of vortices of two-dimensional (2D) incompressible fluid flow over a wall-mounted plate. Following the accuracy verification of the AMR method using the benchmarks of 2D lid-driven cavity flows and backward-facing step flows, this study considers the application of the AMR method to the flow over a wall-mounted plate. The AMR method refines a mesh using numerical solutions of the Navier–Stokes equations computed using an open-source flow solver, Navier2D. The AMR is applied to seven test cases considering flows with different Reynolds numbers ([Formula: see text]) and the estimated centers of vortices after the plate are reported. The results show that AMR can capture the location of the center of vortices within the once refined cells. Furthermore, improved estimation of vortex centers is obtained using twice refined meshes. The AMR aims to get a refined mesh which captures the characteristics of flow with required accuracy at a lower computational cost.
... The adaptation algorithm is tested on the laminar steady flow past a square cylinder at Reynolds = 40 and ℎ = 0.1 at zero incidence. The square cylinder test case is a well-known case in the literature, studied among others by Sen et al. in [60] and already used for validation of mesh adaptation algorithms both in the steady and unsteady configurations, by Li et al. [61], Chalmers in [62] and Hoffman et al. in [63]. ...
In this paper, we present a mesh h-adaptation strategy suited for the discontinuous Galerkin formulation of the compressible Navier-Stokes equations on unstructured grids, based on the simplicial remeshing library MMG. A novel a posteriori error estimator, combining the measure of the energy associated with the highest-order modes and the inter-element jumps, is used to build the metric field. The performance of the developed mesh adaptation algorithm is assessed for steady laminar viscous flows past a square cylinder and past a NACA0012 airfoil, and for the unsteady laminar viscous flow past a circular cylinder. The gain in accuracy for a given number of degrees of freedom (DoFs) is demonstrated for p=1, p=2 and p=3 polynomial degrees, with respect to uniformly refined simulations.
... [Li and Wood (2017)] applied the AMR method twice to the initial meshes and the twice refined meshes show that centers of the vortices are held within the twice refined cells. [Li (2017a)] considered flow past a square cylinder over symmetrical domain but the streamlines drawn on the initial mesh are not symmetrical. The symmetry of streamlines on the refined meshes are improved significantly after applying the AMR method once on the initial meshes. ...
Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method refines a mesh using the numerical solution of the Navier–Stokes equations computed on the mesh by an open source software Navier2D which implemented a vertex centered finite volume method (FVM) using the median dual mesh to form control volumes about each vertex. The accuracy is shown by the comparison between vortex center locations calculated from the linearly interpolated numerical solutions and those obtained in the benchmark. The AMR method is proposed based on the qualitative theory of differential equations, and it can be applied to refine a mesh as many times as required and used to seek accurate numerical solutions of the mathematical models including the continuity equation for incompressible fluid or steady-state compressible flow with low computational cost.
... We conduct study with constant boundary and initial conditions at the inlet channel and apply the AMR method twice to the initial meshes. We compare the profiles of the exact horizontal component of the velocity field and the profiles obtained numerically after the flow is well developed at the step [19]. Finally we show the differences between calculated locations of all detachment, reattachment and centres of vortices and the corresponding benchmarks [19]. ...
... We compare the profiles of the exact horizontal component of the velocity field and the profiles obtained numerically after the flow is well developed at the step [19]. Finally we show the differences between calculated locations of all detachment, reattachment and centres of vortices and the corresponding benchmarks [19]. ...
... The computational domain is normalized using $h=1$. The outputs in terms of detachments, reattachments and locations of vortices are also normalized and compared with the results in Erturk [19]. ...
Identifying accurate centers of vortices of fluid flow is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method by the benchmarks of 2D lid-driven cavity flows, this paper shows the accuracy verification by the benchmarks of 2D backward facing step flows. The AMR method refines a mesh using the numerical solutions of the Navier-Stokes equations calculated on the mesh by an open source software Navier2D which implemented a vertex centered finite volume method (FVM) using the median dual mesh to form control volumes about each vertex. The accuracy of the refined meshes is shown by the centers of vortices given in the benchmarks being held within the twice refined cells. The accuracy is also shown by the comparison between vortex center locations calculated from the linearly interpolated numerical solutions and those obtained in the benchmark. The AMR method is proposed based on the qualitative theory of differential equations, and it can be applied to refine a mesh as many times as required and used to seek accurate numerical solutions of the mathematical models including the continuity equation for incompressible fluid or steady-state fluid flow with low computational cost.
The lid-driven cavity flow problem stands as a widely recognized benchmark in fluid dynamics, serving to validate CFD algorithms. Despite its geometric simplicity, the lid-driven cavity flow problem exhibits a complex flow regime primarily characterized by the formation of vortices at the centre and corners of the square domain. This study evaluates the accuracy of the 2D velocity-driven adaptive mesh refinement (2D VDAMR) method in estimating vortex centres in a steady incompressible flow within a 2D square cavity. The VDAMR algorithm allows for an arbitrary number of finite mesh refinements. Increasing the number of successive mesh refinements results in more accurate outcomes. In this paper, the initial coarse uniform grid mesh was refined ten times for Reynolds numbers 100≤Re≤7500. Results show that VDAMR accurately identifies vortex centres, with its findings closely aligning with benchmark data from six literature sources.
