Analysis and application of high order implicit Runge–Kutta schemes to collocated finite volume discretization of the incompressible Navier–Stokes equations

Kazemi-Kamyab, V.; Zuijlen, A.H. van; Bijl, H.

doi:10.1016/j.compfluid.2014.11.025

Cited by 16 publications

(18 citation statements)

References 29 publications

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“…Recently, Komen et al 76 analyzed five numerical algorithms in finite volume collocated grid solvers for the incompressible Navier-Stokes equations for a selection of explicit (and implicit) Runge-Kutta schemes. They demonstrated that the temporal order reduces to approximately one also for the higher order schemes (except for the high-order method of Kazemi, 78 which however turns out to be very dissipative). Therefore, and for simplicity reasons as mentioned in the Introduction, we describe both projection methods (IFM and CFM) with the explicit Euler method 79 (also called Forward Euler) that is, the original Chorin-Temam algorithm.…”

Section: Explicit Projection Methods (Temporal Discretization)mentioning

confidence: 99%

Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

Star

Sanderse

Stabile

et al. 2021

Numerical Methods in Fluids

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A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the ROM level). These are two main advantages compared to existing approaches. The fully discrete FOM is obtained by a finite volume discretization of the incompressible Navier-Stokes equations on a collocated grid, with a forward Euler time discretization. Two variants of the time discretization method, the inconsistent and consistent flux method, have been investigated. The latter leads to divergence-free velocity fields, also on the ROM level, whereas the velocity fields are only approximately divergencefree in the former method. For both methods, stable and accurate results have been obtained for test cases with different types of boundary conditions: a lid-driven cavity and an open-cavity (with an inlet and outlet). The ROM obtained with the consistent flux method, having divergence-free velocity fields, is slightly more accurate but also slightly more expensive to solve compared to the inconsistent flux method. The speedup ratio of the ROM and FOM computation times is the highest for the open cavity test case with the inconsistent flux method.

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Section: Explicit Projection Methods (Temporal Discretization)mentioning

confidence: 99%

Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

Star

Sanderse

Stabile

et al. 2021

Numerical Methods in Fluids

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“…We have to note that face residual vector, R f i ( ) is obtained by the discretized form of a SDIRK stage, as in [4]. KazemiKamyab et al [4] showed that this technique allows to avoid temporal order reduction suffered by several implementation techniques analyzed in the present literature. Lastly in this paper we have used stiffly accurate SDIRK schemes having the following feature: a b sj j = .…”

Section: Singly Diagonally Implicit Runge-kutta Methodsmentioning

confidence: 99%

Development of openfoam solvers for incompressible navier–stokes equations based on high-order runge–kutta schemes

D’Alessandro¹,

Zoppi²,

Binci³

et al. 2016

Int. J. CMEM

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Nowadays open-source CFD codes provide suitable environments for implementation and testing low-dissipative algorithms typically used for turbulence simulation. Moreover these codes produce a reliable tool to test high-fidelity numerics on unstructured grids, which are particularly appealing for industrial applications. Therefore in this work we have developed several solvers for incompressible Navier-Stokes equations (NSE) based on high-order explicit and implicit Runge-Kutta (RK) schemes for time-integration. Note that for NSE space discretization the numerical technology available within OpenFOAM (Open-source Field Operation And Manipulation) library was used.Specifically in this work we have considered explicit RK projected type schemes for index 2 DAE system and L-stable Singly Diagonally Implicit Runge-Kutta (SDIRK) techniques. In the latter case an iterated PISO-like procedure based on Rhie-Chow correction was used for handling pressure-velocity coupling within each RK stage. The accuracy of the considered algorithms was evaluated studying the Taylor-Green vortex. Moreover several benchmark solutions have been computed in order to assess the reliability, the accuracy and the robustness of the presented solvers.

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“…Namely, an incompressible explicit projection method together with the classical fourth order Runge-Kutta (RK) and accelerated third order ARK3 time integration schemes have been implemented in OpenFOAM by Vuorinen et al [43] . Higher order implicit RK schemes have been implemented in OpenFOAM by Kazemi-Kamyab et al [18] , together with an incompressible iterated PISO-based procedure. In addition, they used an alternative face velocity interpolation method in order to preserve the formal order of the applied temporal schemes.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, they used an alternative face velocity interpolation method in order to preserve the formal order of the applied temporal schemes. D'Alessandro et al [10] implemented a slight variant of the approach of Kazemi-Kamyab et al [18] in OpenFOAM. Furthermore, they implemented the incompressible explicit RK-based projection algorithm of Sanderse and Koren [31] .…”

Section: Introductionmentioning

confidence: 99%

A symmetry-preserving second-order time-accurate PISO-based method

et al. 2021

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Analysis and application of high order implicit Runge–Kutta schemes to collocated finite volume discretization of the incompressible Navier–Stokes equations

Cited by 16 publications

References 29 publications

Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

Development of openfoam solvers for incompressible navier–stokes equations based on high-order runge–kutta schemes

A symmetry-preserving second-order time-accurate PISO-based method

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