A time discontinuous Galerkin finite element method for generalized thermo-elastic wave analysis, considering non-Fourier effects

Guo, Pan; Wu, Wenhua; Wu, Zhigang

doi:10.1007/s00707-013-0961-8

Cited by 13 publications

(15 citation statements)

References 17 publications

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“…As previously reported [15], the selection of stiffness proportional and a mass proportional damping coefficient is effective for high-frequency oscillations and low-frequency oscillations, respectively. To filter out the oscillations in the wave-front stage caused by a high-frequency impulse load, an artificial stiffness proportional Rayleigh-type damping scheme is introduced with the following form:…”

Section: Artificial Damping Scheme For Dgfemsupporting

confidence: 56%

Modelling of Generalised Thermoelastic Wave Propagation of Multilayer Material under Thermal Shock Behaviour

Guo

Zhao

2017

Shock and Vibration

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This paper describes a time-discontinuous Galerkin finite element method (DGFEM-) for the generalised thermoelastic problem of multilayer materials subjected to a transient high-frequency heat source. The governing and constitutive relations are presented on the basis of the well-known Lord-Shulman (L-S) theory. A DGFEM-method is developed to allow the general temperaturedisplacement vector and its temporal gradient to be discontinuous at a fixed time . A stiffness proportional artificial damping term is added to the final DG discretisation form to filter out the spurious numerical oscillations in the wave-after stage and at adjacentlayer interfaces. The numerical results show that the present DGFEM-provides much more accurate solutions for generalised thermoelastic coupled behaviour of multilayer structures. Compared with widely used traditional numerical methods (e.g., the Newmark method), the present DGFEM-can effectively capture the discontinuities behaviours of impulsive waves in space in the simulation of high modes and sharp gradients.

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Section: Artificial Damping Scheme For Dgfemsupporting

confidence: 56%

Modelling of Generalised Thermoelastic Wave Propagation of Multilayer Material under Thermal Shock Behaviour

Guo

Zhao

2017

Shock and Vibration

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“…Their work has demonstrated that the Galerkin form of the wave equation can yield accurate and stable results when time-discontinuous space-time elements are used in conjunction with least squares stabilizers. It should be noted that numerical stabilizers are usually problem dependent, Guo et al and Izdpanah et al [33,34].…”

Section: Introductionmentioning

confidence: 99%

Highly accurate space-time coupled least-squares finite element framework in studying wave propagation

2020

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Simulation of stress wave propagation through solid medium is commonly carried using Galerkin weak-form cast over decoupled space and time domains. In this paper, accuracy of this commonly utilized framework is compared to that of the variationally-consistent least-squares form of the wave equation cast over space-time domain. The two formulations are tested for numerical dispersion and numerical diffusion, through two test cases. The first case studies the dispersion in harmonic shear wave propagation through a soil column over a wide range of forcing frequencies. The second test case investigates numerical diffusion in an axial wave propagation generated by constant force; which is removed after a certain time to allow free vibration to take place. Low numerical dispersion and numerical diffusion as well as high rates of convergence are the main advantages of the coupled least-squares (CLS) computational framework; when compared to the decoupled Galerkin (DG) framework. Based on studies presented here, CLS has low dispersion; yielding errors with one to two orders of magnitude less than that of DG. Also, the numerical diffusion present in DG framework causes a %40 error in DG's prediction of the stress-wave intensity. Furthermore, accumulative error during evolution is virtually nonexistent for CLS, whereas, the error steadily increases as the solution evolves in DG framework. It is also demonstrated that CLS feature of temporal meshing allows for faster computations.

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“…e remarkable characteristics of the DG method is that the basic unknown variables together with their temporal derivatives are assumed to be discontinuous at a defined time point and are assumed to be interpolated by third-order Hermite function and linear function in a time step, respectively. We then successfully applied the MDGFEM, based on an additional artificial damping scheme, to simulate heat wave propagation and generalized thermoelastic problems subjected to thermal shock [13,14]. Numerical results demonstrate that the MDGFEM illustrates better performance in numerical simulation of wave propagation in eliminating spurious numerical oscillations and in providing more accurate solutions than that of the traditional time integration method and the DGFEM before being modified.…”

Section: Introductionmentioning

confidence: 99%

A Time-Discontinuous Galerkin Finite Element Method for the Solution of Impact Problem of Gas-Saturated Coal

Zhang

Guo

et al. 2020

Shock and Vibration

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Based on the general Biot theory of saturated porous media, a modified time-discontinuous Galerkin finite element method (MDGFEM) is presented to simulate the structural dynamics and wave propagation problems of gas-saturated coal subjected to impact loading. Numerical results of one dimension and two dimensions show that the present MDGFEM possesses better abilities and provides much more accurate solutions than the traditional Newmark method and previous DGFEM for the impact problem. It can effectively capture the discontinuities of the wave and filter out the effects of spurious numerical oscillation induced by high-frequency impulsive load. The results can provide a technological basis for the research of the prevention of coal and gas dynamic disasters under deep mining. And the method could be useful for the further numerical research of coal-rock-gas coupling problems and coal-gas-heat coupling problems subjected to impact loading.

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A time discontinuous Galerkin finite element method for generalized thermo-elastic wave analysis, considering non-Fourier effects

Cited by 13 publications

References 17 publications

Modelling of Generalised Thermoelastic Wave Propagation of Multilayer Material under Thermal Shock Behaviour

Modelling of Generalised Thermoelastic Wave Propagation of Multilayer Material under Thermal Shock Behaviour

Highly accurate space-time coupled least-squares finite element framework in studying wave propagation

A Time-Discontinuous Galerkin Finite Element Method for the Solution of Impact Problem of Gas-Saturated Coal

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