Precision controllable Gaver-Wynn-Rho algorithm in Laplace transform triple reciprocity boundary element method for three dimensional transient heat conduction problems. (English) Zbl 1464.80024
Summary: In this paper, Laplace transform triple reciprocity boundary element method (LT-TRBEM) is employed to solve the three dimensional transient heat conduction problems. In order to improve the accuracy of the Laplace inversion using Gaver-Wynn-Rho (GWR) algorithm in non-multi-precision computational environment, a precision controllable GWR (PCGWR) algorithm is proposed in the current study. The inversion parameter \(N_L\) will be selected automatically according to inverse transform accuracy. Solutions with very poor precision in GWR will be identified and eliminated by PCGWR to guarantee the inverse transform accuracy. In LT-TRBEM, there is a non-integral term containing fundamental solution in the boundary integral equation (BIE) for domain points. The value of it is infinite and cannot be calculated directly. In order to supplement this shortcoming, a computable BIE for domain points is proposed, the term with infinite value is converted into a known amount of boundary integral. So, we can calculate the domain points’ temperature successfully, and LT-TRBEM can be employed in problems with discontinuous boundary conditions. Three numerical examples were included to demonstrate the performance of the proposed approach. In summary, LT-TRBEM combined with the PCGWR and the new BIE for domain points can capture the transient heat conduction responses efficiently and accurately.
MSC:
| 80M15 | Boundary element methods applied to problems in thermodynamics and heat transfer |
| 65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
Keywords:
transient heat conduction; boundary element method; precision controllable Gaver-Wynn-Rho; triple reciprocity methodReferences:
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