Structure-preserving time integrators for thermodynamics of nonlinear continua.

用于非线性连续体热力学的结构保持时间积分器。

• 批准号: 184296245
• 负责人: Professor Dr.-Ing. Michael Groß
• 金额: --
• 依托单位: Institut für Mechanik und Thermodynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/184296245?language=en
• 关键词: Structure; preserving; time; integrators; thermodynamics

The steady increase of the performance of computers allows nowadays a computational analysis of thermodynamic processes with a full consideration of mutual interactions of coupled physical fields. Hence, these systems can be optimized much faster and cheaper. In numerical simulations of thermodynamic systems, it is therefore important to apply time integrators, which numerically exactly reproduce mutual interactions and, moreover, make the simulation more robust. This is guaranteed if a time discretisation algorithmically reproduce the physical structure, which means structural characteristics as balance laws and constitutive properties are fullfilled exactly in a discrete setting independent of the time discretisation. In comparison to standard time integrators, structure preserving time integrators therefore are able to simulate processes also with a coarse time discretisation.The aim of the submitted research project is to make the designed structure preserving time integrators more user-friendly. The new algorithms should perform an individual adaption of the time discretisation in each coupled field subject to the structure preservation, and at the same time a structure preserving adaption of the spatial finite element mesh. The adaption of the time discretisation is obtained by determining the distribution of interpolation points of temporal shape functions in a given time step.But this p-adaption will not be controlled by numerical errors as usual, but controlled by structure preservation. The finite element adaption in space is based on a calculation of the nodal positions with the balance equation of material forces of the continuum (r-adaption).

随着计算机性能的不断提高，现在可以在充分考虑耦合物理场相互作用的情况下对热力学过程进行计算分析。因此，这些系统可以更快、更便宜地进行优化。因此，在热力学系统的数值模拟中，重要的是应用时间积分器，其在数值上精确地再现相互作用，并且使模拟更鲁棒。如果时间离散化算法再现物理结构，这意味着作为平衡定律和本构性质的结构特征在独立于时间离散化的离散设置中完全满足，则可以保证这一点。与标准时间积分器相比，结构保持时间积分器因此能够模拟过程，也具有粗略的时间discretionation.The提交的研究项目的目的是使设计的结构保持时间积分器更加用户友好。新的算法应执行一个单独的适应的时间离散化在每个耦合领域的结构保护，并在同一时间的空间有限元网格的结构保护适应。时间离散的自适应是通过确定时间形状函数在给定时间步长内的插值点的分布来实现的，但这种p-自适应不受通常的数值误差控制，而是受结构保持控制。空间中的有限元自适应是基于用连续体的材料力的平衡方程（r-自适应）计算节点位置。