The need for high order numerical schemes to model dispersive high frequency acoustic waves in water-filled pipes

Probing fluid pipelines with high frequency transient waves permits high resolution defect detection. For probing frequency above the first cut-off frequency, radial and/or azimuthal modes are excited and plane wave theory does not apply. A two dimensional explicit scheme based on the finite-volumes method uses an approximate Riemann solver to evaluate hyperbolic terms. To minimize numerical dissipation and reduce computations, higher order schemes using weighted essential non-oscillatory cell-reconstruction and the Runge-Kutta method for time evolution are developed and tested. The parabolic (viscous) part is spatially discretized by second-order finite differences and operator splitting (fourth-order Runge-Kutta) for simultaneous evaluation of inviscid and viscous parts. The characteristic boundary condition for dispersive high frequency waves is also studied. Radial wave propagation from rapid valve closure is discussed and results show the propagation of radial waves if closure time induced frequency is higher than cut-off frequencies.