An explicit gas kinetic scheme algorithm on non-uniform Cartesian meshes for GPGPU architectures

Lenz, Stephan; Geier, Martin; Krafczyk, Manfred

doi:10.1016/j.compfluid.2019.04.011

Cited by 8 publications

(2 citation statements)

References 37 publications

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“…The GKS is implemented on Cartesian meshes, which are beneficial for automated mesh generation. For mesh refinement the quad tree type method proposed by [49] is used.…”

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

confidence: 99%

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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“…The GKS is implemented on Cartesian meshes, which are beneficial for automated mesh generation. For mesh refinement the quad tree type method proposed by [49] is used.…”

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

confidence: 99%

Estimating Local Function Complexity via Mixture of Gaussian Processes

Panknin¹,

Chmiela²,

Müller³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…To extend present method to unstructured meshes, accurate and robust interpolation method is crucial. In previous gas kinetic model, linear least squares regression (LLSR) was proved to be an efficient and accurate way for interpolation [30][31][32]. In present work, LLSR is applied in spatial interpolation.…”

Section: Introductionmentioning

confidence: 99%

A simplified discrete unified gas kinetic scheme for incompressible flow

Zhong

Zou

Pan

et al. 2020

Preprint

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The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows which combines the benefits of both Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By reconstruction of gas distribution function using particle velocity characteristic line, flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with reconstruction stage on a whole time step instead of half time step in original DUGKS. Using temporal/spatial integral Boltzmann Bhatnagar-Gross-Krook (BGK) equation, the transformed distribution function with inclusion of collision effect is constructed. The macro and mesoscopic fluxes of the cell on next time step is predicted by reconstruction of transformed distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on next time step can be updated through its macroscopic flux. Equilibrium distribution function on next time step can also be updated. Gas distribution function is updated by FV scheme through its predicted mesoscopic flux in a time step. Compared with the original DUGKS, the computational process of the proposed method is more concise because of the omission of half time step flux calculation. Numerical time step is only limited by the Courant-Friedrichs-Lewy (CFL) condition and relatively good stability has been preserved. Several test cases, including the Couette flow, lid-driven cavity flow, laminar flows over a flat plate, a circular cylinder, and an airfoil, as well as micro cavity flow cases are conducted to validate present scheme. The numerical simulation results agree well with the references' results.

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A new gas kinetic BGK scheme based on the characteristic solution of the BGK model equation for viscous flows

Zhao

Fang

2023

Computers & Mathematics with Applications

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An explicit gas kinetic scheme algorithm on non-uniform Cartesian meshes for GPGPU architectures

Cited by 8 publications

References 37 publications

Estimating Local Function Complexity via Mixture of Gaussian Processes

Estimating Local Function Complexity via Mixture of Gaussian Processes

A simplified discrete unified gas kinetic scheme for incompressible flow

A new gas kinetic BGK scheme based on the characteristic solution of the BGK model equation for viscous flows

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