تقرير
Relaxation methods and finite element schemes for the equations of visco-elastodynamics
| العنوان: | Relaxation methods and finite element schemes for the equations of visco-elastodynamics |
|---|---|
| المؤلفون: | Simeoni, Chiara |
| المساهمون: | Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA) |
| المصدر: | https://hal.science/hal-03232894Test ; 2021. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2021 |
| المجموعة: | HAL Université Côte d'Azur |
| مصطلحات موضوعية: | visco-elastodynamics system, relaxation approximations, finite element schemes, stability and convergence, dissipative effects, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation |
| الوصف: | Work in progress in collaboration with Athanasios E. Tzavaras (King Abdullah University of Science and Technology (KAUST) - Saudi Arabia) and Corrado Lattanzio (University of L'Aquila, Italy) ; We are interested in the numerical simulation of continuum mechanics systems by means of finite element schemes for appropriate relaxation models, which formally arise as hyperbolic singular perturbations of the original equations. Analytical investigations indicate that relaxation provides a dissipative mechanism against the destabilizing effect of nonlinear terms, as well as damping effects on oscillations when assisted by nonlinear response. From a numerical point of view, the utilization of relaxation methods result in discrete systems with linear principal part and the nonlinearity confined to zero order source terms, which is an advantage especially for simulating conservation laws with nonlinear fluxes because it avoids the need for complex Riemann solvers. In addition, the relaxation regularization may prevent from using extra stabilization techniques such as limiters or shock capturing operators. Finite element schemes use piecewise polynomials of arbitrary degree and exhibit higher order consistency error on unstructured meshes, thus producing efficient numerical solvers for multi-dimensional problems. The natural framework for relaxation approximations is offered by the theory of materials with internal variables, which describes the diffusive stress relaxation of the system of visco-elastodynamics through a small dissipative correction as part of a wave operator with finite speed of propagation. In terms of industrial applications, the behavior of viscoelastic materials has a profound influence on their performance to achieve particular goals: for example, viscoelastic shoe insoles are useful in reducing mechanical shocks transmitted to the bones and joints, and the recent introduction of memory foam for mattresses and pillows is another important exploitation. The objective of the study currently conducted is ... |
| نوع الوثيقة: | report |
| اللغة: | English |
| العلاقة: | hal-03232894; https://hal.science/hal-03232894Test; https://hal.science/hal-03232894/documentTest |
| الإتاحة: | https://hal.science/hal-03232894Test https://hal.science/hal-03232894/documentTest |
| حقوق: | http://hal.archives-ouvertes.fr/licences/copyrightTest/ |
| رقم الانضمام: | edsbas.AFCBC249 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |