A fictitious-source formulation for direct numerical simulation of turbulent boundary layers in prescribed pressure gradients

Abstract A fictitious-source formulation is introduced for prescribing general streamwise pressure-gradient distributions at the boundary-layer edge in compressible boundary-layer simulations whileretaining a flat Cartesian domain. The method constructs a thermodynamically consistent quasi-one-dimensional isentropic outer-flow target, from which compatible mass, streamwise-momentum andtotal-energy source terms are derived. These replace the streamtube expansion or contraction associatedwith the target evolution and are blended out towards the boundary layer, leaving its internal dynamicsunforced. The formulation is validated for low-speed adverse- and favourable-pressure-gradient turbulentboundary layers against expanding- and contracting-domain reference simulations sharing the same flatlower wall. The prescribed edge-velocity development, wall friction, mean velocity profiles and turbulentstresses are reproduced with close quantitative agreement. At Mach 2, forced flat-wall configurationsare compared with curved-wall boundary layers at closely matched edge-velocity distributions. Theprescribed edge velocity and pressure are recovered with only small deviations, whereas the differentwall and streamline geometries produce measurable differences in boundary-layer development despitethe closely matched outer-flow histories. A momentum-integral analysis including streamline-curvatureterms further underlines the coupled nature of the curvature influence, which affects several contributionsthrough the modified boundary-layer development rather than appearing as a single explicit curvatureterm. The method thereby enables pressure-gradient distributions to be prescribed independently ofwall geometry, particularly in compressible and supersonic boundary layers.