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

Abstract

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

Structure‐preserving methods for a coupled port‐Hamiltonian system of compressible non‐isothermal fluid flow

“…The structures of the variational formulations in 2.2 and 3.2 do not differ in general, except for the the function spaces and algebraic equations. Thus, the same structure-preserving numerical methods as introduced in the [7,8] and [2] are applied to the concluding numerical example.…”