TY - GEN
T1 - A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D
AU - Benedusi, Pietro
AU - Hupp, Daniel
AU - Arbenz, Peter
AU - Krause, Rolf
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - We present a parallel and efficient multilevel solution method for the nonlinear systems arising from the discretization of Navier–Stokes (N-S) equations with finite differences. In particular we study the incompressible, unsteady N-S equations with periodic boundary condition in time. A sequential time integration limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. Time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus can improve parallel scalability. To achieve fast convergence, we used a spacetime multigrid algorithm with a SCGS smoothing procedure (symmetrical coupled Gauss–Seidel, a.k.a. box smoothing). This technique, proposed by Vanka (J Comput Phys 65:138–156, 1986), for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We used numerical experiments to analyze the scalability and the convergence of the solver, focusing on the case of a pulsatile flow.
AB - We present a parallel and efficient multilevel solution method for the nonlinear systems arising from the discretization of Navier–Stokes (N-S) equations with finite differences. In particular we study the incompressible, unsteady N-S equations with periodic boundary condition in time. A sequential time integration limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. Time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus can improve parallel scalability. To achieve fast convergence, we used a spacetime multigrid algorithm with a SCGS smoothing procedure (symmetrical coupled Gauss–Seidel, a.k.a. box smoothing). This technique, proposed by Vanka (J Comput Phys 65:138–156, 1986), for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We used numerical experiments to analyze the scalability and the convergence of the solver, focusing on the case of a pulsatile flow.
UR - http://www.scopus.com/inward/record.url?scp=84998893199&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-39929-4_26
DO - 10.1007/978-3-319-39929-4_26
M3 - Conference contribution
AN - SCOPUS:84998893199
SN - 9783319399270
SN - 9783319399270
SN - 9783319399270
T3 - Lecture Notes in Computational Science and Engineering
SP - 265
EP - 273
BT - Numerical Mathematics and Advanced Applications ENUMATH 2015
A2 - Manguoglu, Murat
A2 - Karasozen, Bulent
A2 - Tezer-Sezgin, Munevver
A2 - Ugur, Omur
A2 - Tezer-Sezgin, Munevver
A2 - Manguoglu, Murat
A2 - Ugur, Omur
A2 - Goktepe, Serdar
A2 - Ugur, Omur
A2 - Tezer-Sezgin, Munevver
A2 - Manguoglu, Murat
A2 - Karasozen, Bulent
A2 - Karasozen, Bulent
A2 - Goktepe, Serdar
A2 - Goktepe, Serdar
PB - Springer Verlag
T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015
Y2 - 14 September 2015 through 18 September 2015
ER -