Local multiquadric RBF meshless scheme for radiative heat transfer in strongly inhomogeneous media

Sun, Jing; Luo, Kang; Yi, Hong-Liang; Tan, He‐Ping

doi:10.1016/j.jqsrt.2015.05.012

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…For example, Gu et al 6 adopted several techniques to reduce the instability of the numerical solutions, including the use of upwind domains, nodal refinement and support domain enlargement. Sun et al 7 also used the upwind scheme to improve the stability of the numerical solution for the heat conduction problem in an inhomogeneous medium, while Fornberg et al 8 proposed a filter mechanism to eliminate the instability in solving the purely advection PDEs with the RBF‐FD method. However, all these methods require a constant update of the local support domains according to the flow velocities to ensure that there is a larger number of adjacent nodes in the upwind direction.…”

Section: Introductionmentioning

confidence: 99%

An improved meshfree scheme based on radial basis functions for solving incompressible Navier–Stokes equations

Xie

Zhao

Rubinato

et al. 2021

Numerical Methods in Fluids

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In this paper, an improved meshfree scheme based on radial basis functions (RBFs) is provided for solving the incompressible viscous Navier–Stokes equations and two enhancements are proposed to mitigate the typical numerical oscillations. The first one is the combination of the RBFs‐based finite difference (RBF‐FD) method with the semi‐Lagrangian RBFs (SLM‐RBF), with the former being used for the viscous diffusion term and pressure Poisson equation and the latter being used for the advection term. The second enhancement is a regularization term that constructs smooth constraints for RBFs interpolations instead of clipping operations. The capability of the proposed scheme in mitigating numerical fluctuations is demonstrated by validating it against the one‐dimensional (1‐D) advection problem and the advection–diffusion problem with step field functions. The overall performance of the proposed scheme is also validated by the lid‐driven cavity flow and laminar flow around a circular cylinder, showing good agreement with the existing results, indicating that the proposed scheme has good stability in both temporal and spatial domains.

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Section: Introductionmentioning

confidence: 99%

An improved meshfree scheme based on radial basis functions for solving incompressible Navier–Stokes equations

Xie

Zhao

Rubinato

et al. 2021

Numerical Methods in Fluids

View full text Add to dashboard Cite

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Generalized source Finite Volume Method for radiative transfer equation in participating media

Zhang

Wang

2017

Journal of Quantitative Spectroscopy and Radiative Transfer

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Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

et al. 2018

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The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

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Local multiquadric RBF meshless scheme for radiative heat transfer in strongly inhomogeneous media

Cited by 4 publications

References 30 publications

An improved meshfree scheme based on radial basis functions for solving incompressible Navier–Stokes equations

An improved meshfree scheme based on radial basis functions for solving incompressible Navier–Stokes equations

Generalized source Finite Volume Method for radiative transfer equation in participating media

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

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