Coupling of an Eulerian near-wall solver and a Vortex Particle-Mesh method for the simulation of 2D moving bodies

Two broad categories of methods are used in the computational fluid dynamics community: Eulerian and Lagrangian methods. Eulerian methods are well-suited to capture sharp gradients, such as boundary layers, as the mesh can be body-fitted and anisotropic. On the other hand, Lagrangian methods are typically isotropic (as using particles) and have low numerical dispersion and diffusion. In particular, Vortex Particle-Mesh methods (i.e. with regular redistribution of the particle using a background mesh) have shown to be very efficient and accurate in the simulation of wake flows over long distances. One could then want to couple a Eulerian method to a vortex method, in order to achieve a high resolution of the flow near the solid boundaries, while being able to simulate the wake far downstream in an efficient way. We present the weak coupling between a Eulerian, Finite Difference (FD) solver, and a hybrid Vortex Particle-Mesh (VPM) method to perform Direct Numerical Simulation (DNS) of incompressible 2D flows past bodies, as validated by Billuart et al. [1]. The FD solver uses the staggered grid method for the velocity-pressure formulation of the Navier-Stokes equations, while the VPM solver uses the vorticity-velocity formulation of those equations. As such, the methodology can be used to investigate the flow past impulsively started (or stopped) bodies at various Reynolds numbers. Thanks to the body-fitted grid, we capture accurately the flow details in the near-wall region (the development of the boundary layers near the wall, their separation, the near wake-development) and the wall-resolved quantities (pressure and shear stress) used to evaluate the aerodynamic forces and moments. We further extended the methodology to handle flow past arbitrarily moving bodies: the FD mesh, attached to the body, now moves relatively to static background VPM mesh. We will present some applications of this methodology to moving cylinders and airfoils. Computational resources have been provided by the supercomputing facilities of the Université catholique de Louvain (CISM/UCL) and the Consortium des Équipements de Calcul Intensif en Fédération Wallonie Bruxelles (CÉCI) funded by the Fond de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under convention 2.5020.11 and by the Walloon Region. The present research benefited from computational resources made available on Lucia, the Tier-1 supercomputer of the Walloon Region, infrastructure funded by the Walloon Region under the grant agreement n°1910247.

Affiliations

UCLouvainSST/IMMC/TFL - Thermodynamics and fluid mechanics

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Marchal, Y., Billuart, P., Duponcheel, M., Winckelmans, G., & Chatelain, P. (2025). Coupling of an Eulerian near-wall solver and a Vortex Particle-Mesh method for the simulation of 2D moving bodies. IX International Conference on Particle-based Methods - Particles 2025, Barcelone. https://hdl.handle.net/2078.5/260594