Structure-preserving time integrators for thermodynamics of nonlinear continua.

• Applicant: Professor Dr.-Ing. Michael Groß
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: from 2010 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 184296245

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).

• DFG Programme: Research Grants