Cfd Uncertainty Quantification Using Stochastic Spectral Methods - Exemplary Application to a Buoyancy-Driven Mixing Process

Wenig, Philipp J.; Klein, Markus; Kelm, Stephan

doi:10.2139/ssrn.4157189

Cited by 2 publications

(11 citation statements)

References 27 publications

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“…S D accounts for the enthalpy transport due to diffusive mass transport and the associated correction of the heat conduction [19]. The effective dynamic viscosity µ ef f is the sum of the molecular and subgrid-scale viscosity.…”

Section: Governing Equationsmentioning

confidence: 99%

“…T N µ, σ 2 , a, b denotes a truncated normal distribution with a and b as the lower and upper bounds. Further information about the case setup and regarding the definition of uncertain parameters can be found in [19].…”

Section: Case Setup and Uncertaintiesmentioning

confidence: 99%

“…In the present work, the aim of the UQ method development for the description of stochastic processes is to produce accurate and efficient HDMR models that can represent stochastic results effectively while minimizing the number of required computations. Therefore, the PCE-HDMR approach, which combines Cut-HDMR with PCE, is applied to an intricate dynamic CFD system for the first time and continues the work of Wenig et al [16][17][18][19] in the field of uncertainty quantification for buoyancy-driven mixing processes between two miscible fluids. The PCE-HDMR approach basically involves the construction of high-dimensional stochastic models through a number of low-dimensional submodels, which are built by PCE.…”

Section: Introductionmentioning

confidence: 99%

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CFD Uncertainty Quantification using PCE-HDMR – Exemplary Application to a Buoyancy-Driven Mixing Process

Wenig

Kelm

Klein

2023

Preprint

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For the investigation of uncertainties in high dimensional spaces of computationally expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are needed. These methods should provide accurate and efficient High-Dimensional Model Representations (HDMR) of stochastic results using a reasonable number of calculations. Therefore, the PCE-HDMR approach is utilized to qualify appropriate UQ methods for large-scale computations in the field of Computational Fluid Dynamics (CFD). This technique is a combination of Cut-HDMR, a hierarchical decomposition modeling approach, with Polynomial Chaos Expansion (PCE). To demonstrate its effectiveness, the PCE-HDMR methodology in conjunction with complementary modeling techniques is applied for the UQ analysis of a buoyancy-driven mixing process between two miscible fluids within the Differentially Heated Cavity (DHC) of aspect ratio 4. The results include a thorough probabilistic representation of time-dependent response quantities that comprehensively describe the mixing process. The stochastic models are derived from Large Eddy Simulations (LES) using PCE HDMR and the Sparse Grid Method (SGM), which serves as a reference for the results from PCE-HDMR. The results show that PCE-HDMR provides accurate statistics of the modeled time-dependent stochastic processes and shows good agreement with the SGM reference. Thus, PCE-HDMR indicates great potential for UQ of technical-scale computations due to its efficiency and flexibility in the construction of stochastic models.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Case Setup and Uncertaintiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CFD Uncertainty Quantification using PCE-HDMR – Exemplary Application to a Buoyancy-Driven Mixing Process

Wenig

Kelm

Klein

2023

Preprint

Self Cite

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“…As a result, the stochastic approximation of random responses in the presence of uncertainties might be impeded. To address this issue, Stochastic Model Composition (SMC), or Random Field Composition (RFC), was introduced in [4], as a novel approach for modeling time-dependent stochastic processes with function composition. In the present work, the SMC methodology is employed to perform UQ of the buoyancy-induced mixing process.…”

Section: Stochastic Model Compositionmentioning

confidence: 99%

“…The impact of these uncertainties on responses needs to be quantified. Therefore, by using a generic test case, different methods were initially developed and qualified as suitable for the application to engineering applications [1,2,3,4]. Stochastic spectral methods, such as PCE and KLE, were proven a promising approach and form the basis for the approximation of stochastic results in the present work.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification of a Industrial Scale CFD Application Using Stochastic Spectral Methods

Wenig,

Kelm,

Klein

2023

5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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Accurate prediction of flow phenomena is crucial for a wide range of industrial and scientific applications. However, due to the complexity of many fluid systems, even state-of-theart Computational Fluid Dynamics (CFD) simulations involve various sources of uncertainty, which need to be quantified. Therefore, this work focuses on the Uncertainty Quantification (UQ) of a CFD simulation of a technical scale experiment, which investigates buoyancy-driven mixing processes between two miscible fluids. The CFD model is subject to uncertainties in initial and boundary conditions, as well as in thermo-physical properties. Since computational runs of the CFD model are computationally expensive, the uncertainty analysis requires the use of efficient methods. For this reason, stochastic spectral methods, such as Polynomial Chaos Expansion (PCE) and Karhunen-Loève Expansion (KLE), are applied along with novel approaches like Stochastic Model Composition (SMC) for the uncertainty quantification of responses. Fluctuations due to turbulence are identified as considerable source of uncertainty and are modeled with tailored stochastic models. Results include a comprehensive probabilistic representation of response quantities with probability density functions (PDFs), statistical moments, variance-based decomposition and supplementary error estimates of the underlying stochastic models. This enables well-founded result interpretation and informed decision making. The UQ results show that the uncertain input parameters considerably affect the duration of the mixing process. Through the investigations, the applied UQ methods were tested on an engineering application and demonstrate great potential as a viable technique for uncertainty quantification in technical-scale computations.

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Cfd Uncertainty Quantification Using Stochastic Spectral Methods - Exemplary Application to a Buoyancy-Driven Mixing Process

Cited by 2 publications

References 27 publications

CFD Uncertainty Quantification using PCE-HDMR – Exemplary Application to a Buoyancy-Driven Mixing Process

CFD Uncertainty Quantification using PCE-HDMR – Exemplary Application to a Buoyancy-Driven Mixing Process

Uncertainty Quantification of a Industrial Scale CFD Application Using Stochastic Spectral Methods

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