RT Journal Article
T1 A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes
A1 Busto Ulloa, Saray
A1 Río Martín, Laura del
A1 Vázquez Cendón, María Elena
A1 Dumbser, Michael
K1 All Mach number flow solver
K1 Pressure-based projection method
K1 Finite element method
K1 Finite volume scheme
K1 Semi-implicit scheme on unstructured staggered meshes
K1 ADER methodology
AB In this paper a new hybrid semi-implicit finite volume / finite element (FV/FE) scheme is presented for the numerical solution of the compressible Euler and Navier–Stokes equations at all Mach numbers on unstructured staggered meshes in two and three space dimensions. The chosen grid arrangement consists of a primal simplex mesh composed of triangles or tetrahedra, and an edge-based / face-based staggered dual mesh. The governing equations are discretized in conservation form. The nonlinear convective terms of the equations, as well as the viscous stress tensor and the heat flux, are discretized on the dual mesh at the aid of an explicit local ADER finite volume scheme, while the implicit pressure terms are discretized at the aid of a continuous finite element method on the nodes of the primal mesh. In the zero Mach number limit, the new scheme automatically reduces to the hybrid FV/FE approach forwarded in [1] for the incompressible Navier–Stokes equations. As such, the method is asymptotically consistent with the incompressible limit of the governing equations and can therefore be applied to flows at all Mach numbers. Due to the chosen semi-implicit discretization, the CFL restriction on the time step is only based on the magnitude of the flow velocity and not on the sound speed, hence the method is computationally efficient at low Mach numbers. In the chosen discretization, the only unknown is the scalar pressure field at the new time step. Furthermore, the resulting pressure system is symmetric and positive definite and can therefore be very efficiently solved with a matrix-free conjugate gradient method.In order to assess the capabilities of the new scheme, we show computational results for a large set of benchmark problems that range from the quasi incompressible low Mach number regime to compressible flows with shock waves.
PB Elsevier
SN 0096-3003
YR 2021
FD 2021-08-01
LK https://hdl.handle.net/10347/38193
UL https://hdl.handle.net/10347/38193
LA eng
NO Busto, Río-Martín, Vázquez-Cendón, & Dumbser. (2021). A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes. Applied Mathematics and Computation, 402. https://doi.org/10.1016/J.AMC.2021.126117
NO This work was financially supported by the Italian Ministry of Education, University and Research (MIUR) in the framework of the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications and via the Departments of Excellence Initiative 2018–2022 attributed to DICAM of the University of Trento (grant L. 232/2016). Furthermore, LR and MEV have received funding by Spanish MCIU under project MTM2017-86459-R and by FEDER and Xunta de Galicia funds under the ED431C 2017/60 project. SB was also funded byINdAM via a GNCS grant for young researchers and by a UniTN starting grant of the University of Trento. SB, LR and MD are members of the GNCS group of INdAM.
DS Minerva
RD 24 abr 2026