Coordinatore del Gruppo
Gennaro Coppola - Professore di Fluidodinamica (ING-IND/06)
Settore ERC del Gruppo
PE8_1 Aerospace engineering
PE8_5 Fluid mechanics, hydraulic-, turbo-, and piston engines
Componenti del Gruppo
Carlo De Michele - Ph.D. Student
Activity outlines

The Computational Fluid Dynamics group is active in both theoretical and applied research in the numerical simulation of fluid-dynamics problems. Recent activity has been focused on the design and assessment of robust and accurate numerical methods for both compressible and incompressible flows.

As regards incompressible flows, the group has developed and tested pseudo-symplectic Runge–Kutta time-integration methods for the incompressible Navier–Stokes equations with applications to the numerical simulation of turbulent flows. In contrast to fully energy-conserving, implicit methods, these are explicit schemes of order p that preserve kinetic energy to order q, with q >p. Use of explicit methods with improved energy-conservation properties is appealing for convection-dominated problems, especially in case of direct and large-eddy simulation of turbulent flows.

Other contributions are focused on the development of Fast-Projection methods for the discretization of incompressible Navier-Stokes methods. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods proposed by the group are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and have been applied to some of the most commonly employed RK schemes.

As regards compressible flows, the most important contributions have been made in the broad field of structure-preserving numerical methods, with the aim of design robust and accurate methods for turbulent simulations. General conditions for the local and global conservation of primary (mass and momentum) and secondary (kinetic energy) invariants for finite-difference and finite-volume type formulations have been recently derived in a general setting for transport equations relevant to fluid-dynamics problems. This activity completes a systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the convective terms in the compressible flow equations which was previously conducted by the group and which provides a quite complete characterization of kinetic energy preserving discrete formulations for compressible Euler equations. This analysis has also conducted to novel splittings with exact discrete preservation of kinetic energy. Other recent contributions have been made on the conservation properties of the discretizations of various formulations of the system of compressible Euler equations for shock-free flows, with special focus on the treatment of the energy equation and on the induced discrete equations for other thermodynamic quantities (e.g. entropy).

Prof. A. E. P. Veldman, University of Groningen
Prof. F. Capuano, Technical University of Catalonia
Prof. X. Trias, Technical University of Catalonia
Selected publications

• G. Coppola and A.E.P.Veldman "Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flow" J. Comput. Phys. 475, 111879, 2023.
• C. De Michele and G. Coppola "Numerical treatment of the energy equation in compressible flows simulations" Comput. Fluids 250, 105709, 2023.
• C. de Michele, F. Capuano, G. Coppola, "Fast-Projection Methods for the Incompressible Navier–Stokes Equations"Fluids Volume 5, Issue 4, Article number 222, 2020.
• G. Coppola, F. Capuano, L. De Luca, "Discrete energy-conservation properties in the numerical simulation of the Navier-Stokes equations" Applied Mechanics Reviews, 71 (1), 010803, 2019.
• G. Coppola, F. Capuano, S. Pirozzoli, L. de Luca, "Numerically stable formulations of convective terms for turbulent compressible flows" J. Comput. Phys. 382, pp. 86-104, 2019.
• E. M. De Angelis,G. Coppola, F. Capuano, L. de Luca, "Derivation of new staggered compact schemes with application to Navier-Stokes equations" Applied Sciences , 8 (7), 1066, 2018.
• M. d'Aquino, F. Capuano, G. Coppola, C. Serpico, and I. D. Mayergoyz, "Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics" AIP Advances 8, 056014, 2018.
• M. d'Aquino, F. Capuano, G. Coppola, C. Serpico and I.D. Mayergoyz, "Pseudo-symplectic numerical schemes for Landau-Lifshitz dynamics" Physica B: Condensed Matter 549, 98- 101, 2018.
• F. Capuano, G. Coppola, L. Randez and L. de Luca, "Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties" J. Comput. Phys. 328, pp. 86-94, 2017.
• F. Capuano, G. Coppola, M. Chiatto and L. de Luca, "Approximate projection method for the incompressible Navier-Stokes equations" AIAA J. 54, pp. 2179-2182, 2016.
• F. Capuano, G. Coppola, G. Balarac, L. de Luca "Energy preserving turbulent simulations at a reduced computational cost" J. Comp. Phys. 298, pp. 480-494, 2015.
• F. Capuano, G. Coppola, L. de Luca "An efficient time advancing strategy for energy preserving simulations" J. Comp. Phys. 295, pp. 209-229, 2015.