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| Home > Publications database > A Parallel-in-Time Spectral Deferred Correction Finite Element Method for Unsteady Incompressible Viscous Flow Problems |
| Conference Presentation (After Call) | FZJ-2025-00176 |
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2024
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Please use a persistent id in citations: doi:10.34734/FZJ-2025-00176
Abstract: Simulating unsteady viscous flows by numerically solving the time-dependent Navier-Stokes equations is a computationally expensive challenge. However, while spatial parallelization can reduce computational costs, temporal integration of time-sensitive applications often requires a very large number of time steps. Therefore, more parallelism in numerical time-stepping schemes for further speedup is required. The present work proposes and analyzes a parallel-in-time spectral deferred correction method for the solution of the unsteady incompressible viscous flow problems governed by parabolic–elliptic PDEs. The temporal discretization employs the Spectral Deferred Correction (SDC) method in parallel, which iteratively computes a higher-order collocation solution by conducting a sequence of correction sweeps through the utilization of a low-order time-stepping technique. A standard finite element method is considered for spatial discretization due to its ability to accurately capture complex geometries and boundary conditions. The goal of this work is to illustrate and analyze the properties of the parallel-in-time method through numerical experiments including flows past a cylinder (using the standard DFG 2D-3 benchmark) which is selected as an unsteady flow example.
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