Local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems

Qian, Lingzhi; Chen, Jinru; Feng, Xinlong

doi:10.1002/num.22116

Cited by 7 publications

(5 citation statements)

References 30 publications

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“…Besides, we compare the effectiveness of the presented schemes with the first order schemes [26]. Furthermore, by a practical problem (submarine mountain problem), which has been proposed in [23], the performance of the schemes (3.1) and (3.2) is illustrated. Finally, the coast mountain or cliff problem [3] is applied to illustrate the performance of the presented schemes.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In this example, we check the presented schemes (3.1) and (3.2) on a practical problem with a submarine mountain problem [23]. We take ν 1 = 0.005 and ν 2 = 0.01 in this example.…”

Section: Submarine Mountain Problemmentioning

confidence: 99%

“…In fact, the fluid-fluid interaction model can be seen as one of them arises in many important scientific, engineering and industrial applications, such as heterogeneous of blood flow [8] and atmosphere-ocean interaction [20][21][22]. Due to the practical importance of the fluid-fluid interaction problem, there has been a lot of attention recently paid to the development of accurate and efficient numerical methods; see, e.g., [5,[16][17][18][19]23] among many others. Besides, Bresch and Koko [4] have presented a numerical simulation of the considered model by using an operator-splitting method and optimizationbased nonoverlapping domain decomposition methods.…”

Section: Introductionmentioning

confidence: 99%

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Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Li¹,

null²,

He³

2023

JCM

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In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the secondorder backward differentiation formula for temporal discretization, the second-order Gear's extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

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Section: Numerical Experimentsmentioning

confidence: 99%

“…In this example, we check the presented schemes (3.1) and (3.2) on a practical problem with a submarine mountain problem [23]. We take ν 1 = 0.005 and ν 2 = 0.01 in this example.…”

Section: Submarine Mountain Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Li¹,

null²,

He³

2023

JCM

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“…In 2021, they replaced the AV step of the AV‐DDC method in Reference [14] by subgrid artificial viscosity(SAV) step to propose a SAV‐DDC method [15], for smooth solutions, the SAV‐DDC method was second‐order in time and showed advantages over AV‐DDC method. Considering the case of low viscosities in both atmosphere and ocean fields, Qian et al adopted a local projection stabilized method to control spurious oscillations in the velocities and used a method of characteristics type to avert the difficulties caused by the nonlinear terms in Reference [16]. In 2020, Aggul et al combined the GA approach with a projection‐based variational multiscale stabilization (VMS) to propose a GA‐VMS method for coupled Navier–Stokes system [17].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of two decoupled algorithms for a parabolic two domain problem

Shan

Zhang

2022

Numerical Methods Partial

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To investigate the fluid-fluid interaction problem, we study two first-order in time, decoupled algorithms for a coupling system. This system consist of two heat equations, which are coupled by a condition that allows energy to pass back and forth across the interface. The first scheme is a combination of the three-level implicit method with the coupling terms treated by the explicit leap-frog method. Under a time step size condition, we prove that it is stable and first-order convergent. To remove the time step size condition, we modify the treatment of the coupling interface term and propose a second scheme. Instead of making the interface term explicitly, we only lag the variable in the different subdomain onto the previous time step. As expected, the second scheme is proved to be stable and convergent unconditionally. Since both schemes only require the solution of two decoupled heat equations at each time step. Hence, they are efficient in computation and can be easily implemented by using legacy codes. The numerical tests also confirm our theoretical results. KEYWORDSa parabolic two domain problem, atmosphere-ocean interaction, partitioned time stepping method

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“…A local projection stabilized and characteristic decoupled scheme aiming at the fluid-fluid interaction problems was proposed. It can reflect the extensive applications of the local projective method [32]. More recently, the parameters of the local projection filtering method were optimized and applied to noisily observed variations in light intensity between the star and its observer [33].…”

Section: Introductionmentioning

confidence: 99%

Fault Diagnosis of Rolling Bearing Based on a Novel Adaptive High‐Order Local Projection Denoising Method

Yuan

Song

2018

Complexity

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Rolling bearings are vital components in rotary machinery, and their operating condition affects the entire mechanical systems. As one of the most important denoising methods for nonlinear systems, local projection (LP) denoising method can be used to reduce noise effectively. Afterwards, high-order polynomials are utilized to estimate the centroid of the neighborhood to better preserve complete geometry of attractors; thus, high-order local projection (HLP) can improve noise reduction performance. This paper proposed an adaptive high-order local projection (AHLP) denoising method in the field of fault diagnosis of rolling bearings to deal with different kinds of vibration signals of faulty rolling bearings. Optimal orders can be selected corresponding to vibration signals of outer ring fault (ORF) and inner ring fault (IRF) rolling bearings, because they have different nonlinear geometric structures. The vibration signal model of faulty rolling bearing is adopted in numerical simulations, and the characteristic frequencies of simulated signals can be well extracted by the proposed method. Furthermore, two kinds of experimental data have been processed in application researches, and fault frequencies of ORF and IRF rolling bearings can be both clearly extracted by the proposed method. The theoretical derivation, numerical simulations, and application research can indicate that the proposed novel approach is promising in the field of fault diagnosis of rolling bearing.

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Local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems

Cited by 7 publications

References 30 publications

Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Numerical analysis of two decoupled algorithms for a parabolic two domain problem

Fault Diagnosis of Rolling Bearing Based on a Novel Adaptive High‐Order Local Projection Denoising Method

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