Efficiency of diagonally implicit Runge-Kutta time integration schemes in incompressible two-phase flow simulations

Kim, Young Jun; Bouscasse, Benjamin; Seng, Sopheak; Touzé, David Le

doi:10.1016/j.cpc.2022.108415

Cited by 5 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…40 The Taylor-Green vortices are benchmark flows often used to test the numerical methods for solving problems of vortical dynamics. 61,62 The comparison of calculations with results obtained through other numerical methods previously validated and physical experiments was also provided. This includes simulating the formation of a dipole structure and the evolution of an initial elliptical vortex patch.…”

Section: Validation Of the Methodsmentioning

confidence: 99%

“…To verify the particle‐spectral method, a closed, rectangular domain

D

without a flow‐through boundary was used, with an initial vorticity distribution corresponding to Taylor‐Green flow 40 . The Taylor–Green vortices are benchmark flows often used to test the numerical methods for solving problems of vortical dynamics 61,62 . The comparison of calculations with results obtained through other numerical methods previously validated and physical experiments was also provided.…”

Section: Description Of the Particle‐spectral Approachmentioning

confidence: 99%

See 1 more Smart Citation

An extended and improved particle‐spectral method for analysis of unsteady inviscid incompressible flows through a channel of finite length

Говорухин

2022

Numerical Methods in Fluids

View full text Add to dashboard Cite

This paper addresses the development of a method to simulate and analyze unsteady flows of incompressible and inviscid fluids in rectangular channels. Mathematically, the flow problem formulates as Euler equations in terms of the stream function and vorticity. The normal velocity and the vorticity aregiven at the inlet of the channel, and only the normal velocity is specified at the outlet. The particle-spectral method describes the vorticity field change in a Lagrangian sense by dynamics of marker particles and an Eulerian description of the velocity field using the global Galerkin approximation. The method involves the subdivision of flow domain on rectangular cells; the approximation of vorticity distribution in cells by least-squares method; Galerkin coefficients calculation using analytical integration on space variables. For time integration, the five-stage Runge-Kutta method of the third accuracy order and the sixth one of symplecticity with adaptive step size control uses. The extension of the particle-spectral approach comprises algorithms for fluid flows qualitative analysis jointly with the time simulation of unsteady flows. This includes the trajectories of marker particles calculation, computing the particle's residence time in the channel, kinetic energy dynamics, and algorithms for analyzing the dynamics and mixing of vortex patches. Test calculations based on reference solutions showed the effectiveness and good accuracy of the particle-spectral approach. Using the developed method the dynamics of one and two initial vortex patches in the channel were investigated. We found the final state of their long-time dynamics is time-periodic or quasi-periodic movements. The application of qualitative analysis algorithms demonstrates these final states produce a chaotic scattering of fluid particles in the flow-through zone of the channel. K E Y W O R D Sflowing through channel, inviscid incompressible fluid, particle-spectral method, vortex dynamics

show abstract

Section: Validation Of the Methodsmentioning

confidence: 99%

“…To verify the particle‐spectral method, a closed, rectangular domain

D

Section: Description Of the Particle‐spectral Approachmentioning

confidence: 99%

An extended and improved particle‐spectral method for analysis of unsteady inviscid incompressible flows through a channel of finite length

Говорухин

2022

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…The simulations were conducted using the 0.99 off-centered Crank-Nicolson scheme, identified as the most efficient time-integration scheme for wave simulation in a previous study [37]. For turbulence transport, however, the implicit Euler time-integration scheme was employed to enhance numerical stability.…”

Section: Numerical Configurationsmentioning

confidence: 99%

High-Order Spectral Irregular Wave Generation Procedure in Experimental and Computational Fluid Dynamics Numerical Wave Tanks, with Application in a Physical Wave Tank and in Open-Source Field Operation and Manipulation

Kim,

Canard,

Bouscasse

et al. 2024

JMSE

Self Cite

View full text Add to dashboard Cite

The accurate generation of a target sea state in numerical or experimental wave tanks is a fundamental line of research for the ocean engineering community. It guarantees the quality and relevance of wave–structure interaction tests. This study presents a reproducible irregular wave generation and qualification procedure, accounting for the nonlinear aspects of wave propagation. It can be used for both numerical simulation and experiments. The presented numerical and experimental results are obtained from the OpenFOAM solver and the Ecole Centrale Nantes wave tank facilities, respectively. The procedure comprises two steps: First, the wavemaker motion is calibrated numerically to generate the target wave spectrum at the position of interest. This is achieved with a wavemaker-equipped nonlinear potential flow solver. The open-source HOS-NWT solver, based on the high-order spectral method, was employed in this study. Then, the corrected wavemaker motion is used directly in the experimental wave tank. OpenFOAM simulations were performed to generate waves with the relaxation method, using wave elevation and velocity field data from HOS-NWT. The procedure was finally tested for mild and extreme breaking sea states. The waves generated by the HOS-NWT solver, the experiment, and the OpenFOAM simulation were compared from both stochastic and deterministic perspectives.

show abstract

“…In the early development stage, most Runge-Kutta methods are conditionally stable, such as the modified Euler method [21] and the fourth-order fourthstage Runge-Kutta method [21]. At present, the diagonally/fully implicit Runge-Kutta methods [22][23][24][25][26] with unconditional stability have been constructed, and the fully implicit s-stage Runge-Kutta methods [25,26] can reach up to 2sth-order accuracy. But the improvement in accuracy is realized at a dramatic increase in computational cost, so these higher-order schemes are not very practical.…”

Section: Introductionmentioning

confidence: 99%

A three-sub-step composite method for the analysis of rigid body rotations with Euler parameters

Xing

2023

Nonlinear Dyn

View full text Add to dashboard Cite

This paper proposes a composite method for the analysis of rigid body rotation based on Euler parameters. The proposed method contains three sub-steps, wherein for keeping as much low-frequency information as possible the first two sub-steps adopt the trapezoidal rule, and the four-point backward interpolation formula is used in the last sub-step to flexibly control the amount of high-frequency dissipation. On this basis, in terms of the relation between Euler parameters and angular velocity, the stepping formulations of the proposed method are further modified for maximizing the accuracy of the angular velocity. For the analysis of rigid body rotation, the accuracy of the proposed method can converge to second-order, and the amount of its high-frequency dissipation can smoothly range from one (conservative scheme) to zero (annihilating scheme). Additionally, in the proposed method, the constraints at the displacement and velocity levels are strictly satisfied, and the numerical drifts at the acceleration level can be effectively eliminated. Several benchmark rigid body rotation problems show the advantages of the proposed method in stability, accuracy, dissipation, efficiency, and energy conservation.

show abstract

Efficiency of diagonally implicit Runge-Kutta time integration schemes in incompressible two-phase flow simulations

Cited by 5 publications

References 21 publications

An extended and improved particle‐spectral method for analysis of unsteady inviscid incompressible flows through a channel of finite length

An extended and improved particle‐spectral method for analysis of unsteady inviscid incompressible flows through a channel of finite length

High-Order Spectral Irregular Wave Generation Procedure in Experimental and Computational Fluid Dynamics Numerical Wave Tanks, with Application in a Physical Wave Tank and in Open-Source Field Operation and Manipulation

A three-sub-step composite method for the analysis of rigid body rotations with Euler parameters

Contact Info

Product

Resources

About