Stability preserving approximations of a semilinear hyperbolic gas transport model
Provides theoretical guarantees for stability preservation in numerical approximations of gas transport models, relevant for pipeline network simulations.
The paper proves that solutions of a semilinear damped wave equation for gas transport converge exponentially to steady states, and shows that Galerkin approximations preserve this decay behavior uniformly.
We consider the discretization of a semilinear damped wave equation arising, for instance, in the modeling of gas transport in pipeline networks. For time invariant boundary data, the solutions of the problem are shown to converge exponentially fast to steady states. We further prove that this decay behavior is inherited uniformly by a class of Galerkin approximations, including finite element, spectral, and structure preserving model reduction methods. These theoretical findings are illustrated by numerical tests.