RT Journal Article
T1 An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes
A1 Boscheri, Walter
A1 Busto Ulloa, Saray
A1 Dumbser, Michael
K1 All Mach number flow solver
K1 Pressure-based projection method
K1 Virtual element method
K1 Finite volume scheme
K1 Asymptotic preserving
K1 High order in space and time
AB We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the operator splitting of the compressible Navier–Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are discretized implicitly with the aid of a virtual element method (VEM). Consequently, the time step restriction of the overall algorithm depends only on the mean flow velocity and not on the fast pressure waves nor on the viscous eigenvalues. As such, the proposed methodology is well suited for the solution of low Mach number flows at all Reynolds numbers. Moreover, the scheme is proven to be globally energy conserving so that shock capturing properties are retrieved in high Mach number flows while being only linearly implicit in time. To reach high order of accuracy in time and space, an IMEX Runge–Kutta time stepping strategy is employed together with high order spatial reconstructions in terms of CWENO polynomials and virtual element space basis functions. The chosen discretization techniques allow the use of general polygonal grids, a useful tool when dealing with complex domain configurations. The new scheme is carefully validated in both the incompressible limit and the high Mach number regime through a large set of classical benchmarks for fluid dynamics, assessing robustness and accuracy.
PB Elsevier
SN 0045-7825
YR 2025
FD 2025
LK https://hdl.handle.net/10347/40750
UL https://hdl.handle.net/10347/40750
LA eng
NO Boscheri, W., Busto, S., & Dumbser, M. (2025). An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes. Computer Methods in Applied Mechanics and Engineering, 433. https://doi.org/10.1016/J.CMA.2024.117502
NO WB received financial support by Fondazione Cariplo and Fondazione CDP (Italy) under the project No. 2022–1895 and by the Italian Ministry of University and Research (MUR) with the PRIN Project 2022 No. 2022N9BM3N. SB acknowledges the financial support from the Spanish Ministry of Science, Innovation and Universities (MCIN), the Spanish AEI (MCIN/AEI/ 10.13039/501100011033) and European Social Fund Plus under the project No. RYC2022-036355-I; from FEDER and the Spanish Ministry of Science, Innovation and Universities under project No. PID2021-122625OB-I00; and from the Xunta de Galicia (Spain) under project No. GI-1563 ED431C 2021/15. MD was funded by the Italian Ministry of Education, University and Research (MIUR) in the frame of the Departments of Excellence Initiative 2018–2027 attributed to DICAM of the University of Trento (grant L. 232/2016) and in the frame of the PRIN 2022 project High order structure-preserving semi-implicit schemes for hyperbolic equations. MD was also co-funded by the European Union NextGenerationEU (PNRR, Spoke 7 CN HPC) .
DS Minerva
RD 26 abr 2026