The Taylor–Green vortex represents an exact solution of the Navier–Stokes equations in (Formula presented.). In this work, an approximation of this solution in two spatial dimensions is proposed for weakly compressible flows. These flows are characterized by small compressibility (or, equivalently, by a small Mach number) and are often employed in computational fluid dynamics to approximate the behaviour of incompressible Newtonian fluids. In this framework, the proposed solution is expected to be a useful benchmark for numerical solvers that implement the weakly compressibility approximation. To this end, some numerical examples are reported in the final section of this work.
Weakly Compressible Approximation of the Taylor–Green Vortex Solution
Matteo Antuono
Primo
;Salvatore MarroneUltimo
2025
Abstract
The Taylor–Green vortex represents an exact solution of the Navier–Stokes equations in (Formula presented.). In this work, an approximation of this solution in two spatial dimensions is proposed for weakly compressible flows. These flows are characterized by small compressibility (or, equivalently, by a small Mach number) and are often employed in computational fluid dynamics to approximate the behaviour of incompressible Newtonian fluids. In this framework, the proposed solution is expected to be a useful benchmark for numerical solvers that implement the weakly compressibility approximation. To this end, some numerical examples are reported in the final section of this work.File | Dimensione | Formato | |
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Stud Appl Math - 2024 - Antuono - Weakly Compressible Approximation of the Taylor Green Vortex Solution.pdf
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