A Clebsch-based multi-symplectic discretization for smooth isentropic compressible Euler flows

Long-time approximation of smooth inviscid compressible flow is often degraded by artificial dissipation even when shocks are absent. We develop a structure-preserving discretization of the isentropic compressible Euler equations by combining a generalized Clebsch canonicalization with a multi-symplectic Birkhoffian formulation. The construction yields skew-symmetric structural matrices and a fully discrete local geometric balance for a centered periodic spatial operator coupled to implicit midpoint time integration, while multiple Clebsch pairs extend the representation of rotational states. Unit-modulus amplification is established for the propagating subspace of the reduced single-pair linearized periodic problem. Across the benchmark set, the method retains its additional geometric structure with competitive smooth-flow fidelity and case-dependent low-dissipation behavior. The scope is restricted to smooth periodic flows; shocks, arbitrary topology, and nonperiodic boundaries require further development.