Model reduction techniques for frequency averaging in radiative heat transfer

Pinnau, René; Schulze, Alexander

doi:10.1016/j.jcp.2007.04.024

Cited by 13 publications

(7 citation statements)

References 23 publications

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“…Using equation (18) in equation (16), the approximation of the unassembled nonlinear load f u is given by…”

Section: Udeim Methodsmentioning

confidence: 99%

“…On this basis, Falkiewicz and Cesnik 17 demonstrated that a POD basis identified a priori remains available for the solution of linear heat transfer problem with the change of boundary conditions. Pinnau and Schulze 18 adopted POD to construct a reduced-order model in combination with the well-known SPn model for frequency averaging in radiative heat transfer. Big errors appeared at the boundary of the structure.…”

Section: Introductionmentioning

confidence: 99%

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Reduced-order models for radiative heat transfer of hypersonic vehicles

Yan

Jing

Yun

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part G:

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Aerothermoelastic analysis of hypersonic vehicles is a complex multidisciplinary coupling problem. Thus, accurate modeling of varying disciplines with low computational cost is necessary. This work developed a tractable approach-based reduced-order modeling technology to solve the radiative thermal transfer problem in a hypersonic simulation. A method that combines proper orthogonal decomposition and unassembled discrete empirical interpolation method is developed to construct the reduced-order modeling. First, high-dimensional original systems are projected on the optional basis generated by proper orthogonal decomposition, and the nonlinear term is further approximated by unassembled discrete empirical interpolation method. Then, a numerical integration method for the solution of the reduced system of nonlinear differential equations is provided. Case studies that use a classical hypersonic control surface model, in which the time history and spatial distribution of the thermal load are known a priori, are conducted to validate the accuracy and efficiency of the reduced-order modeling methodology and to assess the robustness of the reduced-order modeling for thermal solution. Results indicate the ability of reduced-order modeling to reduce the nonlinear system size with reasonable accuracy.

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“…Using equation (18) in equation (16), the approximation of the unassembled nonlinear load f u is given by…”

Section: Udeim Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced-order models for radiative heat transfer of hypersonic vehicles

Yan

Jing

Yun

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part G:

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show abstract

“…Second, these data are used to determine the laser input amplitude following the procedure described in Section 4.2. The amplitude of the excitation is assumed not known, and it is approximated following a piecewise linear approximation with n fit D 50 (i.e., a uniform mesh of 51 nodes each 20 ms), see (27). Figure 14 shows the synthetically generated temperature at the monitoring point (left) and a comparison (right) between the approximated nodal values (blue markers) and the reference amplitude (solid red line).…”

Section: Amplitude Identificationmentioning

confidence: 99%

“…Finally, it is important to note that in spite of the large amount of scientific contributions using a frequency domain description in solid dynamics, this approach is not standard, to the author's knowledge, for thermal models subjected to dynamical forced thermal loads. Certainly, time domain approximations of thermal models are both efficient and robust, and moreover, model order reduction is successfully applied in this setting [19][20][21][22][23][24][25][26], whereas frequency domain approaches for thermal studies are scarce [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Real‐time monitoring of thermal processes by reduced‐order modeling

Aguado

Huerta

Chinesta

et al. 2014

Numerical Meth Engineering

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SUMMARYThis work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.

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“…In the field of radiative transfer, such model reduction techniques have been applied by Pinnau and Schultze [16] for treating the spectral dependence of the radiative intensity. They used a POD method to model the radiative properties of glass and compared their approach to the Weighted-Sum-of-Grey-Gas (WSGG) method and a simple frequency averaging.…”

mentioning

confidence: 99%