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arXiv · 2603.12992

Discretization of the Burgers' equation as a port-Hamiltonian system

Lorenzo Agostini·Michel Fournié·Ghislain Haine
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Abstract

The numerical simulation of the inviscid Burgers' equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced, leading to the viscous Burgers' equation. In this work, port-Hamiltonian formulations for both the inviscid and the viscous Burgers' equations are proposed, enabling a representation that incorporates both convective and dissipative effects. Boundary control and observation are naturally handled within this framework. Applying a dedicated finite element method, a finite-dimensional port-Hamiltonian system is derived. The relationship between time step, spatial resolution, and viscosity required to achieve numerical stability is analyzed. Numerical experiments validate the effectiveness of the approach.

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Lorenzo Agostini, Michel Fournié, Ghislain Haine. 2026-03-13. Discretization of the Burgers' equation as a port-Hamiltonian system. https://arxiv.org/abs/2603.12992

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