Tikhonov based well-conditioned asymptotic waveform evaluation technique for heat conduction / Md. Sohel Rana - Md. Sohel, Rana (2015)
The dual-phase-lag (DPL) heat transfer model is a very stiff partial differential equation which is the mixed derivative of time-space that makes it hard to tackle accurately. For fast transient solution of heat conduction model based on a moment matching technique, researcher generally takes one of two approaches. The first is to linearize the DPL heat conduction equation, where required to introduce extra degree of freedom. The second approach is to work directly using asymptotic waveform evaluation (AWE). But the AWE method is unattractive because the moment matching techniques is intrinsically ill conditioned. In this dissertation, two well-conditioned schemes have developed to reduce the instability of AWE. Furthermore, Fourier heat transfer model and non-Fourier heat transfer model with DPL have analysed by using Tikhonov based well condition asymptotic wave evaluation (TWCAWE) and finite element model (FEM). The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique has successfully used to predict the accurate and stable temperature responses without the loss of initial high frequency responses. To reduce the increased computational time by Tikhonov based AWE using ML (AWE-ML), another Tikhonov based well-condition scheme called mass effect (AWE-ME) is introduced. AWE-ME showed more stable and accurate temperature spectrum in comparison to asymptotic waveform evaluation (AWE) and also partial Pade AWE without sacrificing the computational time. But the results obtained from AWE-ME scheme are not accurate as AWE-ML. The TWCAWE method is presented here to study the Fourier and non-Fourier heat conduction problems with various boundary conditions. In this work, a novel TWCAWE method is proposed to overwhelm ill-conditioning of the AWE method for thermal analysis and also presented for time-reliant problems. The TWCAWE method is capable to evade the instability of AWE and also efficaciously approximates the initial high frequency and delay similar as well-established numerical method, such as Runge-Kutta (R-K). Furthermore, TWCAWE method is found 1.2 times faster than the AWE and also 4 times faster than the traditional R-K method.