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Directly Simulation of Second Order Hyperbolic Systems in Second Order Form via the Regularization Concept

Communications in Computational Physics 2016年第6期20卷 86-135页

作者： Hassan Yousefi seyed shahram ghorashi Timon Rabczuk Division of Computational Mechanics Ton Duc Thang UniversityHo Chi Minh CityViet Nam a2 Institute of Structural Mechanics Bauhaus-Universitat Weimar99423 WeimarGermany Research Training Group 1462 Bauhaus-UniversitatWeimar99423WeimarGermany Faculty of Civil Engineering Ton Duc Thang UniversityHo Chi Minh CityViet Nam.

We present an efficient and robustmethod for stresswave propagation problems(second order hyperbolic systems)having discontinuities directly in their second order *** to the numerical dispersion around discontinuities and lack of the inherent dissipation in hyperbolic systems,proper simulation of such problems are *** proposed idea is to denoise spurious oscillations by a post-processing stage from solutions obtained from higher-order grid-based methods(e.g.,high-order collocation or finite-difference schemes).The denoising is done so that the solutions remain higher-order(here,second order)around discontinuities and are still free from spurious *** this purpose,improved Tikhonov regularization approach is *** means to let data themselves select proper denoised solutions(since there is no pre-assumptions about regularized results).The improved approach can directly be done on uniform or non-uniform sampled data in a way that the regularized results maintenance continuous derivatives up to some desired *** is shown how to improve the smoothing method so that it remains conservative and has local estimating *** confirm effectiveness of the proposed approach,finally,some one and two dimensional examples will be *** will be shown how both the numerical(artificial)dispersion and dissipation can be controlled around discontinuous solutions and stochastic-like results.

关键词： Second order hyperbolic systems Tikhonov regularization Numerical(artificial)dispersion

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