A carrier-wave factored one-way Navier--Stokes method for boundary-layer instability modelling

Abstract

We present M-OWNS, a spatial marching method that combines the carrier-wave factoring of the parabolised stability equations (PSE) with a recursive one-way Navier--Stokes (OWNS-R) projection framework. A distinct numerical resolution and efficiency advantage is offered by the approach, in modelling disturbance and instability state evolution. A spectral resolution comparison analysis shows that to leading order, for any excited eigenfunction whose eigenvalue lies closer to the carrier wavenumber than to the origin, the wave-factored system resolves the mode at a coarser streamwise numerical step size relative to the unfactored system. A non-iterating variant, with the carrier wavenumber determined from the base flow, temporal frequency and spanwise wavenumber alone, achieves equivalent resolution accuracy at identical per-step cost to unfactored OWNS. For the fixed-carrier variant, M-OWNS reduces the total solve count by factors of two to eight relative to unfactored OWNS across the test cases considered, with larger reductions possible when the iterated closure condition of PSE is suitable. The method is validated across incompressible and subsonic flat-plate boundary-layers, three-dimensional crossflow disturbances, and a Mach~4.5 hypersonic boundary-layer with four forcing configurations: eigenfunction inlet forcing, wall suction/blowing, multi-mode freestream forcing and randomised inlet forcing. The wall suction/blowing case is validated against a fully elliptic linear harmonic Navier--Stokes solver. For deterministic forcing scenarios, M-OWNS captures disturbance amplitudes, acoustic radiation fields, and modal synchronisation sequences at coarser streamwise resolution than unfactored OWNS. Under broadband randomised forcing, M-OWNS resolves mixed-mode disturbance development at half the numerical cost relative to standard OWNS.