Local least–squares element differential method for solving heat conduction problems in composite structures

Gao, Xiao‐Wei; Zheng, Yong-Tong; Fantuzzi, Nicholas

doi:10.1080/10407790.2020.1746584

Cited by 19 publications

(4 citation statements)

References 32 publications

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“…The research is varied according to the interests of the authors, such as the fractional order heat equation in higher space-Time dimensions [2], its numerical resolution [3], and application for heat spreading of electronic components [4]. For numerical resolution of heat equation in various conditions, Local leastsquares element differential method is used to solve heat conduction problems in composite structures [5]. Recently, regarding the problems of realization on the site related to the use of heat sources as well as the optimization of energy consumption, a one-dimensional model is used by Tlili et al [6] to research the belongings of different functional and geometrical parameters on energy consumption of flat distance direct contact membrane distillation (DCMD) for solar desalination tasks.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Heat Transfer in Bilayer, and Three-Layer Materials

Sahabi¹,

Balaska²

2023

Fluid Dynamics &Amp; Materials Processing

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The heat transfer equation is used to determine the heat flow by conduction through a composite material along the real axis. An analytical dimensionless analysis is implemented in the framework of a separation of variables method (SVM). This approach leads to an Eigenvalues problem that is solved by the Newton's method. Two types of dynamics are found: An unsteady condition (in the form of jumps or drops in temperatures depending on the considered case), and a permanent equilibrium (tending to the ambient temperature). The validity and effectiveness of the proposed approach for any number of adjacent layers is also discussed. It is shown that, as expected, the diffusion of the temperature is linked to the ratio of the thermo-physical properties of the considered layers and their number.

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Section: Introductionmentioning

confidence: 99%

Unsteady Heat Transfer in Bilayer, and Three-Layer Materials

Sahabi¹,

Balaska²

2023

Fluid Dynamics &Amp; Materials Processing

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“…Over the past several years, there has been an amount of work concerning meshless methods. The research work on the meshless methods includes Smooth Particle Hydrodynamics (SPH), distance basis function (RBF), Diffuse Element Method (DEM), Element Free Galerkin Method (EFG), Meshless weighted least-squares (MWLS), Least Square Element Differentiation Method (LSEDM) [4], etc. However, these methods sometimes could not achieve the optimal balance of accuracy and computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Finite Difference with the Physics-informed Neural Network for solving PDE in complex geometries

Zixue¹,

Wei²,

Zhou³

et al. 2022

Preprint

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The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study proposes the hybrid finite difference with the physics-informed neural network (HFD-PINN) to fully use the domain knowledge. The main idea is to use the finite difference method (FDM) locally instead of AD in the framework of PINN. In particular, we use AD at complex boundaries and the FDM in other domains. The hybrid learning model shows promising results in experiments. To use the FDM locally in the complex boundary domain and avoid the generation of background mesh, we propose the HFD-PINN-sdf method, which locally uses the finite difference scheme at random points. In addition, the signed distance function is used to avoid the difference scheme from crossing the domain boundary. In this paper, we demonstrate the performance of our proposed methods and compare the results with the different number of collocation points for the Poisson equation, Burgers equation. We also chose several different finite difference schemes, including the compact finite difference method (CDM) and crank-nicolson method (CNM), to verify the robustness of HFD-PINN. We take the heat conduction problem and the heat transfer problem on the irregular domain as examples to demonstrate the efficacy of our framework. In summary, HFD-PINN, especially HFD-PINN-sdf, are more instructive and efficient, significantly when solving PDEs in complex geometries.

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“…In recent years, Gao et al [11][12][13][14][15][16][17][18][19][20] proposed a new strong-form numerical method called element differential method (EDM). Like traditional FEM, EDM also uses isoparametric elements to discretize the computational domain and approximate physical variables.…”

Section: Introductionmentioning

confidence: 99%

“…Dynamic viscosity coefficient of the fluid is 1.79 × 10 −5 Pa•s.5. PermeabilityReferring to eqn(19),…”

mentioning

confidence: 99%

Multi-physics coupling analysis of rope-sealed structures with braided ceramic fibres by element differential method

Zheng¹,

Gao²,

Liu³

et al. 2021

Int. J. CMEM

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With the rapid development of hypersonic vehicles in recent years, high-temperature seal technology has become more and more essential. Recently, a rope-sealed structure with braided ceramic fibres has been designed for hypersonic vehicles. The ceramic fibres in the structure have the characteristics of high temperature strength, so that they make the sealed structure suitable for working under a high temperature. Meanwhile, when subjected to an external force, braided fibres can produce a buffer force at the ceramic interface, so that it can maintain the good performance of the whole sealed structure. But up to now, only a few researches have been conducted on this kind of structures. In this paper, a simplified thermal-mechanical seepage coupling model is proposed to simulate the complicated physical process for this kind of structures. Meanwhile, a new numerical method called element differential method (EDM) is used to calculate the coupling problem because it has great advantages in solving multiphysics coupling problems. What is more, some experiments are used to obtain the leakages when the sealed structure is under service. And finally, by referring the experimental results, the authors establish a series of material parameter relationships for the sealed structure and also verify the reasonability of the proposed multi-physics coupling model.

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Local least–squares element differential method for solving heat conduction problems in composite structures

Cited by 19 publications

References 32 publications

Unsteady Heat Transfer in Bilayer, and Three-Layer Materials

Unsteady Heat Transfer in Bilayer, and Three-Layer Materials

Hybrid Finite Difference with the Physics-informed Neural Network for solving PDE in complex geometries

Multi-physics coupling analysis of rope-sealed structures with braided ceramic fibres by element differential method

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