2019
DOI: 10.1016/j.jcp.2019.07.017
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On some explicit local time stepping finite volume schemes for CFD

Abstract: In this paper, two local time stepping schemes of order two and three in time are proposed. By construction, they are not mass conservative but a correction stage is added to make them conservative. These schemes are compared with some local time stepping schemes existing in the literature (schemes of Constantinescu and Sandu). The comparisons are carried out on various test cases. They prove that our schemes are efficient and our third order local time stepping has a higher time accuracy than the schemes base… Show more

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Cited by 10 publications
(4 citation statements)
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“…The unsteady Reynolds-averaged Navier–Stokes (URANS) equations were numerically solved. Pseudo-transient simulations based on a local time stepping (LTS) numerical scheme [ 26 ] were performed to reduce the computational burden. In this approach the simulation is forced toward a steady state condition similarly to the Reynolds-averaged Navier–Stokes (RANS) approach, but with no need to remove the time derivative in the Navier–Stokes equations, therefore improving stability especially for complex geometries.…”
Section: Methodsmentioning
confidence: 99%
“…The unsteady Reynolds-averaged Navier–Stokes (URANS) equations were numerically solved. Pseudo-transient simulations based on a local time stepping (LTS) numerical scheme [ 26 ] were performed to reduce the computational burden. In this approach the simulation is forced toward a steady state condition similarly to the Reynolds-averaged Navier–Stokes (RANS) approach, but with no need to remove the time derivative in the Navier–Stokes equations, therefore improving stability especially for complex geometries.…”
Section: Methodsmentioning
confidence: 99%
“…However, since fluid and solid regions have, in general, very different physical properties, appropriate time steps can be quite different for these regions. Therefore, methods such as adaptive time stepping 57 or locally varying time stepping 58 schemes can potentially improve the convergence rate and stability.…”
Section: Discussionmentioning
confidence: 99%
“…The numerical solution of the URANS equations is obtained using the OpenFOAM (Open Field Operation And Manipulation) software—an open source C++ modeling toolbox for fluid dynamics related problems (Chen et al., 2014), using the PIMPLE solver algorithm. Coupling PIMPLE with a pseudo‐transient approach based on a local time stepping numerical scheme (Jeanmasson et al., 2019) allows reducing considerably the computational burden. In this approach, the simulation is forced toward a steady state condition similarly to the Reynolds‐averaged Navier–Stokes approach, but with no need to remove the time derivative in the NS equations, therefore improving stability especially for complex geometries.…”
Section: Methodsmentioning
confidence: 99%