Extended Group Finite Element Method for a port‐Hamiltonian Formulation of the Non‐Isothermal Euler Equations

This paper deals with a port-Hamiltonian (pH) formulation of the non-isothermal compressible Euler equations for pipe flow. In pH-framework physical properties, like mass conservation and energy dissipation, are encoded in system structure. Applying structure-preserving Galerkin approximation mixed finite elements space yields nonlinear state-dependent matrices. Assembly these matrices each time step is computationally expensive makes model reduction inefficient, since nonlinearities still depend on full order state. We investigate use extended group element method (EGFEM) to efficiently handle pH structure-preservation. EGFEM separates systems into products state-independent (precomputable) tensor vector nonlinearities, making easily accessible complexity reduction.