A. Colombo’s research while affiliated with University of Bergamo and other places

... Such a localization is then expected to mitigate the non-linear effects that are introduced by considering a transformed state, and therefore maintains the near-optimality of the Kalman update. The current work is motivated by recent positivity-preserving methods in computational fluid simulations that leverage variable transforms [5,6]; however, we note that such techniques have previously been used in the specific domain of Kalman filtering as well [7,8]. ...

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Sequential Ensemble Kalman Filtering of Compressible Flows With Shocks: Enforcing Positivity

... However, pressure equilibrium is essentially a pointwise condition, whereas the correction terms only guarantee integral satisfaction of the auxiliary transport equation(s). Entropy-conservative/entropy-stable DG schemes have been constructed using these correction terms (or similar forms) without relying on SBP operators or entropy-conservative/entropy-stable numerical fluxes [1,26,27,28,29]. The correction terms have also been employed to enforce conservation of total energy while treating entropy density as a state variable [30]. ...

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Conservative, pressure-equilibrium-preserving discontinuous Galerkin method for compressible, multicomponent flows

... To first understand the qualitative flow organisation, figure 5 reports an instantaneous visualisation of the turbulent and shock structures in the flow field using an isosurface of the swirling strength coloured by the streamwise velocity and an isosurface of the shock sensor θ. A video of the flow, generated using in situ visualisation at runtime (Bnà et al. 2023), is linked in the supplementary material. In addition to the shocks associated with the uncontrolled SBLI, another shock system is visible in correspondence with the microramp, which has been characterised extensively in previous works (Della . ...

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High-fidelity simulations of microramp-controlled shock wave/boundary layer interaction

... This kind of approach has been adopted for incompressible flows with variable density, see e.g. 35,36 , and we aim here to consider an artificial compressibility formulation for immiscible, isothermal two-phase flows with gravity. The model equations can be therefore rewritten as follows: ...

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An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation

... For all the isentropic vortexes investigated here, the primitive logarithmic variables, here coupled with the entropy-stable Godunov flux [23], exhibit superior entropy conservation properties with respect to the other variable sets. This improvement is likely due to the positivity of all thermodynamic variables being ensured at the discrete level, which contributes to the correct physical behavior of entropy [28]. 4. For flow speeds ranging from nearly incompressible to subsonic regimes, and for sufficiently high-order dG approximations (e.g., the isentropic vortex with equal perturbation for different free-stream flows and M ∞ = 1.4 · 10 −3 ), the conservative variables show significantly better accuracy compared to all other variable sets, even at large time step sizes. ...

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On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method

... High-order spatial discretisation methods for Computational Fluid Dynamics (CFD), such as the discontinuous Galerkin (dG) methods (Bassi, Botti, et al. 2020;Colombo et al. 2022), can be considered as a viable solution to meet the growing demand for high-fidelity flow simulations, such as for Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). dG methods can provide higher accuracy compared to standard industrial solvers, mainly based on second-order methods, but are still too expensive in terms of simulation time and memory footprint. ...

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Comparison of Different Error Estimators for the p -Adaptive Discontinuous Galerkin Solution of Separated Flows

... However, some recent workshops results and publications seem to indicate that a further increase in accuracy can be obtained by moving to large eddy-simulation (LES) mostly in combination with wall-functions (WFLES) (e.g. Aljure et al. 2018;Colombo et al. 2021;Simmonds et al. 2017)). While successful applications of WFLES have been demonstrated in other areas, like the simulation of high-lift full aircraft configurations (Kiris et al. 2022) (at least on a wind-tunnel scale), the reliability of using such methods in industrial automotive simulations still needs to be established. ...

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Large Eddy Simulations for the Ahmed Car at 25° Slant Angle at Different Reynolds Numbers

... We note that similar observations on the non-polynomial nature of the entropy variables have been made by a variety of different groups in the literature [80,31,19,13,3]. Since ∂u h ∂t ∈ P N D k n for method of lines discretizations, testing the time derivative term in (7) with the projected entropy variables yields ...

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An artificial viscosity approach to high order entropy stable discontinuous Galerkin methods

... We find that quadratic geometry is often sufficient for large deformation with quadratic and cubic solution spaces, and thus these methods can be used with existing meshing and visualization tools, though tailoring to p-version finite element efficiency [57] is beneficial. When cubic and higher order meshes are needed, one can use Gmsh [42] to generate arbitrary order meshes, but many popular mesh formats support at most second order elements and there is a need for improving data representation standards and postprocessing/visualization tools to better support high order geometry and solution fields [58]- [60]. ...

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Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

... While extensive efforts have been made to improve numerical simulation models using mesh refinement techniques in h-adaptivity [36][37][38][39][40], less attention has been given to maintaining a constant number of elements in r-adaptivity [41,42]. This aspect remains relatively underexplored, particularly regarding the effect of r-adaptivity strategies on the quality of the represented data when undergoing dimensionality reduction. ...

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Enhancing data representation in forging processes: Investigating discretization and R-adaptivity strategies with Proper Orthogonal Decomposition reduction