On Solving Two-Dimensional Inverse Heat Conduction Problems Using the Multiple Source Meshless Method

Ku, Cheng-Yu; Xiao, Jing-En; Huang, Wei-Po; Yeih, Weichung; Liu, Chih-Yu

doi:10.3390/app9132629

Cited by 5 publications

(3 citation statements)

References 32 publications

(35 reference statements)

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“…As for the boundary data, it is assigned on both right and left of the spacetime region, as illustrated in Figure 2. To evaluate the accuracy of the proposed approach, the maximum absolute error (MAE) is evaluated by the following equation [32][33][34].…”

Section: Numerical Examplementioning

confidence: 99%

Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

Liu

et al. 2020

Applied Sciences

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This paper presents the modeling of tide–induced groundwater response using the spacetime collocation approach (SCA). The newly developed SCA begins with the consideration of Trefftz basis functions which are general solutions of the governing equation deriving from the separation of variables. The solution of the groundwater response in a coastal confined aquifer with an estuary boundary where the phase and amplitude of tide can vary with time and position is then approximated by the linear combination of Trefftz basis functions using the superposition theorem. The SCA is validated for several numerical examples with analytical solutions. The comparison of the results and accuracy for the SCA with the time–marching finite difference method is carried out. In addition, the SCA is adopted to examine the tidal and groundwater piezometer data at the Xing–Da port, Kaohsiung, Taiwan. The results demonstrate the SCA may obtain highly accurate results. Moreover, it shows the advantages of the SCA such that we only discretize by a set of points on the spacetime boundary without tedious mesh generation and thus significantly enhance the applicability.

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Section: Numerical Examplementioning

confidence: 99%

Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

Liu

et al. 2020

Applied Sciences

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“…Inverse heat transfer problems encompass a spectrum of classifications, including inverse heat conduction problems (the most prevalent), inverse heat convection problems, inverse heat radiation problems, and inverse heat conjugation problems. Researchers have comprehensively explored inverse problems related to heat conduction [1][2][3][4][5][6][7][8][9], heat convection [10][11][12][13][14][15][16], and heat radiation [17][18][19], employing diverse algorithms. However, investigations into inverse conjugate heat transfer problems [20][21][22] remain notably scarce within the available literature.…”

Section: Introductionmentioning

confidence: 99%

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

Huang,

Fang

2024

Mathematics

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In this study, an inverse conjugate heat transfer problem is examined to estimate temporally and spatially the dependent unknown surface heat flux using thermography techniques with a thermal camera in a three-dimensional domain. Thermography techniques encompass a broad set of methods and procedures used for capturing and analyzing thermal data, while thermal cameras are specific tools used within those techniques to capture thermal images. In the present study, the interface conditions of the plate and air domains are obtained using perfect thermal contact conditions, and therefore we define the problem studied as an inverse conjugate heat transfer problem. Achieving the simultaneous solution of the continuity, Navier–Stokes, and energy equations within the air domain, alongside the heat conduction equation in the plate domain, presents a more intricate challenge compared to conventional inverse heat conduction problems. The validity of our inverse solutions was verified through numerical simulations, considering various inlet air velocities and plate thicknesses. Notably, it was found that due to the singularity of the gradient of the cost function at the final time point, the estimated results near the final time must be discarded, and exact measurements consistently produce accurate boundary heat fluxes under thin-plate conditions, with air velocity exhibiting no significant impact on the estimates. Additionally, an analysis of measurement errors and their influence on the inverse solutions was conducted. The numerical results conclusively demonstrated that the maximum error when estimating heat flux consistently remained below 3% and higher measurement noise resulted in the accuracy of the heat flux estimation decreasing. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain.

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“…In recent years, meshfree methods are attracting more and more interests in computational mechanics for its advantages such as good self-adaptability. With the rapid development of meshfree techniques, various problems in science and engineering have been solved by meshfree methods [12][13][14][15]. Meshfree methods have been great potential topics and trends in computational mechanics.…”

Section: Introductionmentioning

confidence: 99%

An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

et al. 2020

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The study of characterizing the stress concentration effects at welds is one of the most important research directions for predicting the fatigue life of welded components. Stress solutions at the weld toe obtained from conventional meshfree methods are strongly influenced by parameters used in the methods as a result of stress singularity. In this study, an improved 2D meshfree radial point interpolation method (RPIM) is proposed for stress concentration evaluation of a welded component. The stress solutions are insensitive to parameters used in the improved RPIM. The improved RPIM-based scheme for consistently calculating stress concentration factor (SCF) and stress intensity factor at weld toe are presented. Our studies provide a novel approach to apply global weak-form meshfree methods in consistently computing SCFs and stress intensity factors at welds.

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On Solving Two-Dimensional Inverse Heat Conduction Problems Using the Multiple Source Meshless Method

Cited by 5 publications

References 32 publications

Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

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