Estimate of Iteration Errors in Computational Fluid Dynamics

Martins, Márcio André Rodrigues; Marchi, Carlos Henrique

doi:10.1080/10580530701790142

Cited by 4 publications

(13 citation statements)

References 11 publications

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“…An alternative method was considered for scenarios where iteration errors demonstrated monotonic convergence. As the number of iterations increased, these errors were observed to decrease on a logarithmic scale [8]. This relationship can be expressed as:…”

Section: Iteration Errormentioning

confidence: 93%

“…Furthermore, Martins and Marchi [8] advocate for precise estimation of iterative errors, emphasizing its relevance in terminating the iterative process once a predefined error threshold for targeted variables is reached. This approach not only conserves computational resources but also prevents the exacerbation of numerical errors due to elevated levels of iterative errors.…”

Section: Introductionmentioning

confidence: 99%

“…Iteration errors are defined as the discrepancy between the direct solution of the discretized equations and the numerical solution at each iteration, with an expectation of a decrement in these errors as the iterative cycle progresses [3]. The estimation of iterative errors is conducted using specific error estimators [3,8,9], a practice of paramount importance in CFD for ensuring solution reliability, resource optimization, and the validation or enhancement of mathematical models. To quantify the error magnitude of the solutions obtained, verification techniques are employed [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…The estimation of iterative errors is conducted using specific error estimators [3,8,9], a practice of paramount importance in CFD for ensuring solution reliability, resource optimization, and the validation or enhancement of mathematical models. To quantify the error magnitude of the solutions obtained, verification techniques are employed [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, it has been observed that iteration errors exhibit a monotonic convergence; as the number of iterations increases, the error decreases logarithmically [9]. A study by Martins and Marchi revealed that the performance of estimators could be categorized into three levels of iteration according to the accuracy of the estimates [8]. However, a common limitation among these methods is the reduced accuracy of estimates at both the initial and final stages of the iterative cycle.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Enhanced Hybrid Methodology for Iteration Error Estimation and Reduction in Heat Transfer Modeling

Dall’Agnol,

Marchi,

Moro

2024

MMEP

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In the realm of numerical simulations for heat transfer problems, the precision of iterative solutions is paramount. This study introduces an innovative hybrid methodology designed to refine iteration error estimation and ameliorate the accuracy of numerical solutions in heat transfer models encompassing diffusion and advection phenomena. Central to this methodology is the development of a novel estimator, predicated on the rate of iterative convergence. The efficacy and versatility of the proposed estimator and the overarching hybrid approach are scrutinized through the analysis of two distinct one-dimensional and a singular two-dimensional heat transfer model. In these applications, it has been demonstrated that the application of the refined methodology significantly enhances the precision of iteration error estimates, particularly in the initial phases of iteration. This improvement in accuracy and reliability of iteration error estimates was consistently observed across all examined models and pertinent variables. Notably, the incorporation of this methodology into existing simulation frameworks is straightforward, marking a substantial advancement in the domain of iteration error estimation. The findings underscore the utility of the proposed hybrid approach in achieving more precise and reliable numerical solutions in a wide array of heat transfer models, thereby contributing to the fidelity and robustness of computational simulations in thermal engineering.

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Section: Iteration Errormentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%