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

Physics of Fluids, vol. 38

Abstract

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.

Authors 4

1. D. Escobar

   Universidad de Santiago de Chile

   Affiliation as printed

   Computational Heat and Fluid Flow Lab, Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile 1 , Región Metropolitana, 9170022 Santiago,

2. Douglas R. Q. Pacheco Aachen Chair for Computational Analysis of Technical Systems (CATS) Chair of Methods for Model‐based Development in Computational Engineering

   RWTH Aachen University

   Affiliation as printed

   Chair for Computational Analysis of Technical Systems and Chair of Methods for Model-based Development in Computational Engineering, RWTH Aachen University 2 , 5206 Aachen,

3. A. Aguirre

   Universidad de Santiago de Chile

   Affiliation as printed

   Computational Heat and Fluid Flow Lab, Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile 1 , Región Metropolitana, 9170022 Santiago,

4. Ernesto F. Castillo

   Universidad de Santiago de Chile

   Affiliation as printed

   Computational Heat and Fluid Flow Lab, Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile 1 , Región Metropolitana, 9170022 Santiago,