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Structure‐preserving discretization of a port‐Hamiltonian formulation of the non‐isothermal Euler equations
Author(s) -
Hauschild Sarah-Alexa,
Marheineke Nicole
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000014
Subject(s) - discretization , mathematics , partial differential equation , euler equations , euler's formula , dissipation , hamiltonian (control theory) , isothermal process , compressibility , compressible flow , mathematical analysis , mathematical optimization , physics , mechanics , thermodynamics
The port‐Hamiltonian (pH) formulation of partial‐differential equations (pdes) and their numerical treatment have been elaborately studied lately. In this context we consider the non‐isothermal flow of a compressible fluid. Starting from the pdes we derive a pH formulation for Euler‐type equations in the weak sense on one pipe. One advantage of pH systems is that fundamental physical properties, like energy dissipation and mass conservation, are encoded in the system structure. Therefore, structure‐preservation during approximation is most important. Based on the weak form we introduce a structure‐preserving Galerkin approximation with mixed finite elements. A numerical example supports the theoretical results.