An analytic wall model suitable for flows in the presence of equilibrium or non-equilbrium effects is derived. The model is predicated upon definition of a new velocity scale that encompasses both viscous and pressure gradient effects, thereby providing a unified approach to simulating separated and attached flows. Asymptotic solutions of the surface layer flow are derived considering the effects of both pressure gradients and convective terms in the streamwise momentum equation resulting in a wall model consistent with flow physics. Within the context of a two-dimensional shock boundary layer interaction at low Reynolds number, the model captures the relevant features, both in the time-mean and unsteady sense. It is demonstrated that inclusion of convective terms in the analytic wall model results in the most accurate representation of the interaction region whereas it over-predicts the wall-shear-stress in equilbrium and near-equilibrium regions. In contrast, considering only pressure-gradient effects in the analytic wall model results in predictions of wall shear stress of increasing accuracy with increasing wall-model/large-eddy-simulation interface distance in all regions of the flow. While the low-Reynolds number simulations were conducted to have a reference wall-resolved simulation, the equilibrium turbulent boundary layer upstream of the interaction displayed a noticeable log-layer region, justifying the separation-of-scales assumption adopted in the wall modeling approach.
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