Multiscale RBF-based central high resolution schemes for simulation of generalized thermoelasticity problems

In this study, average-interpolating radial basis functions (RBFs) are successfully integrated with central high-resolution schemes to achieve a higher-order central method. This proposed method is used for simulation of generalized coupled thermoelasticity problems including shock (singular) waves in their solutions. The thermoelasticity problems include the LS (systems with one relaxation parameter) and GN (systems without energy dissipation) theories with constant and variable coefficients. In the central high resolution formulation, RBFs lead to a reconstruction with the optimum recovery with minimized roughness on each cell: this is essential for oscillation-free reconstructions. To guarantee monotonic reconstructions at cell-edges, the nonlinear scaling limiters are used. Such reconstructions, finally, lead to the total variation bounded (TVB) feature. As RBFs work satisfactory on non-unifdrm cells/grids, the proposed central scheme can handle adapted cells/grids. To have cost effective and accurate simulations, the multiresolution-based grid adaptation approach is then integrated with the RBF-based central scheme. Effects of condition numbers of RBFs, computational complexity and cost of the proposed scheme are studied. Finally, different 1-D coupled thermoelasticity benchmarks are presented. There, perfonnance of the adaptive RBF-based formulation is compared with that of the adaptive Kurganov-Tadmor (KT) second-order central high-resolution scheme with the total variation diminishing (TVD) property.

Wavelet-based iterative data enhancement for implementation in purification of modal frequency for extremely noisy ambient vibration tests in Shiraz-Iran

The main purpose of the present study is to enhance high-level noisy data by a wavelet-based iterative filtering algorithm for identification of natural frequencies during ambient wind vibrational tests on a petrochemical process tower.Most of denoising methods fail to filter such noise properly.Both the signal-to-noise ratio and the peak signal-to-noise ratio are small.Multiresolution-based one-step and variational-based filtering methods fail to denoise properly with thresholds obtained by theoretical or empirical method.Duc to the fact that it is impossible to completely denoise such high-level noisy data,the enhancing approach is used to improve the data quality,which is the main novelty from the application point of view here.For this iterative method,a simple computational approach is proposed to estimate the dynamic threshold values.Hence,different thresholds can be obtained for different recorded signals in one ambient test.This is in contrast to commonly used approaches recommending one global threshold estimated mainly by an empirical method.After the enhancements,modal frequencies are directly detected by the cross wavelet transform(XWT),the spectral power density and autocorrelation of wavelet coefficients.Estimated frequencies are then compared with those of an undamaged-model,simulated by the finite element method.

Response of a spherical cavity in a fully-coupled thermo-poro-elastodynamic medium by cell-adaptive second-order central high resolution schemes

In this study,fully coupled thermo-poroelastic saturated media are simulated by a grid/cell adaptive central high resolution scheme.The central method corresponds to the second order Kurganov-Tadmor(KT)scheme working on adapted cells with the total variation diminishing(TVD)stability condition.The coupled equations include motion,fluid flow,heat flow,continuity condition,and a constitutive equation.The grid/cell adaptation is performed by the interpolating wavelet transform in the multiresolution framework to capture fine scale responses and to obtain a computationally effective solver.With respect to the use of central schemes,the coupled equations should be re-expressed as a system of coupled first-order hyperbolic-parabolic partial differential equations(PDEs)with possible source(load)terms.The system is initially derived in the Cartesian coordinate system,and it is subsequently modified to consider a spherical cavity in isotropic,symmetric,and saturated media in the spherical coordinate system.It is assumed that the cavity boundary is subjected to sudden time-dependent thermal/mechanical sources.Discontinuous propagating fronts develop in the media due to the aforementioned loading.It is challenging to handle these solutions with numerical methods,and special attention is required to prevent/control numerical dispersion and dissipation.Hence,as previously mentioned,adaptive central high resolution schemes are employed in the present study.