A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908815484518400 |
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| author | Escobar, Diego Pacheco, Douglas Aguirre, Alejando Castillo, Ernesto |
| author_facet | Escobar, Diego Pacheco, Douglas Aguirre, Alejando Castillo, Ernesto |
| contents | 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 ensure that the non-residual, term-by-term structure induces dissipation through dynamic subscales suitable for turbulent simulations. The methodology is validated on large-scale external-aerodynamics configurations, including the Ahmed body at Re $ = 7.68\times 10^{5}$ for multiple slant angles, using unstructured tetrahedral meshes ranging from 3 to 40 million elements. Applicability is further demonstrated on a realistic Formula~1 configuration at $U_\infty=56~\mathrm{m/s}$ (201.6~km/h), corresponding to Re $ \approx 10^{6}$. 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 provide an a posteriori consistency indicator, exhibiting finite frequency ranges compatible with inertial-subrange reference slopes in the resolved band and supporting dissipation control in under-resolved regimes within a unified stabilized finite element framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05563 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics Escobar, Diego Pacheco, Douglas Aguirre, Alejando Castillo, Ernesto Fluid Dynamics Numerical Analysis 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 ensure that the non-residual, term-by-term structure induces dissipation through dynamic subscales suitable for turbulent simulations. The methodology is validated on large-scale external-aerodynamics configurations, including the Ahmed body at Re $ = 7.68\times 10^{5}$ for multiple slant angles, using unstructured tetrahedral meshes ranging from 3 to 40 million elements. Applicability is further demonstrated on a realistic Formula~1 configuration at $U_\infty=56~\mathrm{m/s}$ (201.6~km/h), corresponding to Re $ \approx 10^{6}$. 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 provide an a posteriori consistency indicator, exhibiting finite frequency ranges compatible with inertial-subrange reference slopes in the resolved band and supporting dissipation control in under-resolved regimes within a unified stabilized finite element framework. |
| title | A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics |
| topic | Fluid Dynamics Numerical Analysis |
| url | https://arxiv.org/abs/2602.05563 |