Session: 11-02-03: CFD Applications for Optimization and Control II

Paper Number: 166395

Advancing CFD Accuracy: A Richardson Extrapolation-Based Error Analysis 

Computational Fluid Dynamics (CFD) simulations play an increasingly important role in academic research and industrial product development due to the growing availability of computational resources. The accuracy of CFD results is strongly influenced by spatial discretization, i.e. the meshing of the computational domain. To ensure reliable and grid-independent results, potential discretization errors must be quantified. A commonly applied approach for estimating spatial discretization errors is Richardson extrapolation, which relies on systematically generated grids at different resolutions.

In this study, the applicability and accuracy of Richardson extrapolation for estimating spatial discretization errors in CFD are analyzed. The simulations are performed using the commercial CFD solver ANSYS CFX 2024R2. The computational grids are generated with ANSYS ICEM and ANSYS TURBOGRID to ensure high-quality structured meshes. Two distinct CFD models are considered: a backward-facing step, a well-established benchmark case, and a turbomachinery blade passage, a case commonly used in engineering practice. Both models are systematically meshed using hexagonal grids, and the error estimation method is applied to various grid sizes and evaluation quantities. The derived results are comprehensively compared to assess the effectiveness and reliability of the method. Based on these findings, conclusions and recommendations for the practical application of Richardson extrapolation in CFD are provided in detail.

A key aspect of this research is the detailed investigation of the assumptions and limitations associated with Richardson extrapolation. While this approach is widely used in CFD validation and verification studies, its accuracy depends on several factors, including grid refinement ratios, solution smoothness, and numerical dissipation. By carefully analyzing these parameters, this study provides a deeper understanding of the method’s applicability in practical engineering problems.

Furthermore, the influence of turbulence modeling on error estimation is examined. Many CFD simulations rely on Reynolds-Averaged Navier-Stokes (RANS) turbulence models, which introduce additional modeling uncertainties. The interaction between numerical discretization errors and turbulence modeling is explored, highlighting potential challenges when applying Richardson extrapolation in industrial settings.

To enhance the robustness of error quantification, alternative approaches such as grid convergence index (GCI) calculations are included in the analysis. This allows for a comparative assessment of different error estimation techniques, ensuring a more comprehensive evaluation of spatial discretization effects.

The results of this study contribute to a more rigorous understanding of spatial discretization errors in CFD simulations. By providing clear guidelines on the use of Richardson extrapolation, this work aims to support engineers and researchers in improving the reliability of their CFD analyses, ultimately leading to more accurate and trustworthy simulation-based predictions in various application domains.

Presenting Author: Ivana Milanovic University of Hartford

Presenting Author Biography: Full Professor in Fluid Mechanics

Authors:

Manuel Fritsche Coburg University of Applied Sciences
Philipp Epple Coburg University of Applied Sciences
Ivana Milanovic University of Hartford