The Effects of Grid Accuracy on Flow Simulations: A Numerical Assessment

Majid Allahyari,Kianoosh Yousefi,Vahid Esfahanian

doi:10.3390/fluids5030110

Majid Allahyari, Kianoosh Yousefi + Show 1 more

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https://doi.org/10.3390/fluids5030110

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Abstract

High-quality, accurate grid generation is a critical challenge in the computational simulation of fluid flows around complex geometries. In particular, the accuracy of the grids is an effective factor in order to achieve a successful numerical simulation. In the current study, we present a series of systematic numerical simulations for fluid flows around a NACA 0012 airfoil using different computational grid generation techniques, including the standard second-order, fourth-order compact, and Theodorsen transformation approaches, to assess the effects of grid accuracy on the flow solutions. The flow solvers are based on the second- and fourth-order schemes for spatial discretizations and Beam-Warming linearization method for time advancement. The obtained grids, as well as the metrics and the corresponding numerical flow solution for each grid generation technique, are compared and studied in detail. It is demonstrated that the quality and orthogonality of the grids is improved by using the fourth-order compact scheme. Moreover, the numerical assessment showed that the accuracy and the quality of the grids directly influence the numerical flow solutions. Finally, the higher-order accurate flow solvers are found to be more sensitive to the accuracy of the generated grid.

Highlights

One of the most critical subjects in computational fluid dynamics (CFD) simulation and modeling of flows around complex geometries is to generate high-quality grids on the flow region
We first carry out a series of numerical simulations to verify and validate the current high-order compact flow solver against experimental results for fluid flow over a flat plate and a NACA 0012 airfoil
We presented a systematic numerical investigation to examine the influences of grid accuracy on the numerical solution of fluid flow problems with complex-shaped geometries

Summary

Introduction

One of the most critical subjects in computational fluid dynamics (CFD) simulation and modeling of flows around complex geometries is to generate high-quality grids on the flow region. The quality of the generated grid can strongly affect the accuracy of the numerical solution of a partial differential equation system [1,2,3,4]. In the past few decades, it has been established that the generation of high-quality grids is imperative for effective computations, and that can be important as improving the accuracy of the flow solver. Grid generation requires computational mapping from physical to computational space and geometry modeling. Elliptic systems apply an appropriate control function to achieve grid smoothness and orthogonality. Another common method is conformal mapping containing an orthogonal transformation that yields nearly orthogonal grids in the physical space [5]

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