Validation of a two-dimensional gas-kinetic scheme for compressible natural convection on structured and unstructured meshes

Lenz, Stephan; Krafczyk, Manfred; Geier, Martin; Chen, Songze; Guo, Zhaoli

doi:10.1016/j.ijthermalsci.2018.10.004

Cited by 10 publications

(7 citation statements)

References 28 publications

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“…This resolution turns out to be insufficient as the vortices 5 and 6 are not reproduced at all. Here it is to note, that this resolution is very low compared to the 40, 000 cells in [46] and 1, 048, 576 cells in [45].…”

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 87%

“…The Rayleigh number is chosen as 10 7 , which is the highest value for which a stationary solution is reported in the reference [45]. A visualization of the reference flow field at this Rayleigh number based on [46] is shown in Fig. 14.…”

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 99%

“…For the simulation a two-dimensional gas kinetic scheme (GKS) [47], [48] is applied, which was previously shown to yield high quality results for thermal compressible flows and especially the square cavity with differentially heated side walls [46]. The GKS is implemented on Cartesian meshes, which are beneficial for automated mesh generation.…”

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 99%

“…The measured centers by the reference [45] and in our experiment are listed in Tab. V in Appendix F, where we also [46] (with permission). The reference is based on the high resolution simulation from [45].…”

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 99%

“…Fig.14. Reference flow field of the square cavity with differentially heated walls, based on[46] (with permission). The reference is based on the high resolution simulation from[45].…”

mentioning

confidence: 99%

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Estimating Local Function Complexity via Mixture of Gaussian Processes

Panknin¹,

Chmiela²,

Müller³

et al. 2019

Preprint

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Real world data often exhibit inhomogeneity, e.g., the noise level, the sampling distribution or the complexity of the target function may change over the input space. In this paper, we try to isolate local function complexity in a practical, robust way. This is achieved by first estimating the locally optimal kernel bandwidth as a functional relationship. Specifically, we propose Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs the mixture of experts consisting of multinomial kernel logistic regression as a gate and Gaussian process regression models as experts. Using the locally optimal kernel bandwidths, we deduce an estimate to the local function complexity by drawing parallels to the theory of locally linear smoothing. We demonstrate the usefulness of local function complexity for model interpretation and active learning in quantum chemistry experiments and fluid dynamics simulations.

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Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 87%

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 99%

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 99%

Section: Flow In a Square Cavity With Differentially Heated Side Wallsmentioning

confidence: 99%

“…Fig.14. Reference flow field of the square cavity with differentially heated walls, based on[46] (with permission). The reference is based on the high resolution simulation from[45].…”

mentioning

confidence: 99%

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Estimating Local Function Complexity via Mixture of Gaussian Processes

Panknin¹,

Chmiela²,

Müller³

et al. 2019

Preprint

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Analysis and reconstruction of the thermal lattice Boltzmann flux solver

Dai

2022

Numerical Methods in Fluids

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The thermal lattice Boltzmann flux solver (TLBFS) has been proposed as an alternative method to overcome the drawbacks of thermal lattice Boltzmann models. However, as a weakly compressible model, its mechanism of the good numerical stability for high Rayleigh number thermal flows is still unclear. To reveal the mechanism, the present article first derives the macroscopic equations of TLBFS (MEs-TLBFS) with actual numerical dissipation terms by approximating its computational process. By solving MEs-TLBFS with the finite volume method, the reconstructed TLBFS (RTLBFS) is proposed. Detailed analyzes prove that these actual numerical dissipation terms are the mechanism of the good numerical stability of TLBFS for high Rayleigh number thermal flows.More detailed numerical tests indicate RTLBFS has similar performances as TLBFS for stability, accuracy, and efficiency, which further validates the mechanism of the good numerical stability of TLBFS for high Rayleigh number thermal flows.

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