University of Malaga - Spain
We present a reduced-order modelling strategy for nonlinear parametric hyperbolic systems that combines Proper Orthogonal Decomposition (POD) with Discrete Empirical Interpolation (DEIM) for an efficient approximation of nonlinear terms, and introduces PID (Principal-Interval Decomposition) together with a time-averaging approach. The time domain is split into subintervals used for basis construction, and time-averaged states over these subintervals are used to approximate the variables appearing in the nonlinear terms. In addition, the reduced formulation preserves the well-balanced property of the underlying full-order discretisation. Numerical experiments on nonlinear benchmark problems confirm the robustness and efficiency of the proposed reduced-order framework.