A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics

Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation for simulating incompressible flows from laminar to turbulent regimes. The method is embedded in an incremental pressure-correction fractional-step framework and employs a minimal set of stabilization terms, yielding a unified discretization that (i) allows equal-order velocity–pressure interpolation and (ii) provides robust control of convection-dominated dynamics in complex three-dimensional settings. Orthogonal projections are a key ingredient and allow the non-residual, term-by-term structure to induce dissipation through dynamic subscales suitable for turbulence-resolving simulations. The methodology is validated on large-scale external-aerodynamics configurations, including the Ahmed body at Re =7.68×105 for multiple slant angles, using unstructured tetrahedral meshes ranging from 3 to 40 × 106 elements. Applicability is further demonstrated on a realistic Formula 1 configuration at U∞=56 m/s (201.6 km/h), corresponding to Re ≈106. The results show that the proposed stabilized pressure-segregated formulation remains robust at scale and captures key separated-flow features and coherent wake organization. Pointwise velocity and pressure spectra serve as an a posteriori consistency indicator, exhibiting finite frequency ranges compatible with inertial-subrange reference slopes in the resolved band and supporting a physically consistent dissipation behavior in under-resolved regimes within a unified stabilized finite element framework.