Application of local least squares finite element method (LLSFEM) in the interface capturing of two-phase flow systems

Mostafaiyan, Mehdi; Wießner, Sven; Heinrich, Gert; Hosseini, Mahdi; Domurath, Jan; Khonakdar, Hossein Ali

doi:10.1016/j.compfluid.2018.07.007

Cited by 10 publications

(13 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 1, in a structured mesh , shows a typical interface (the solid line) and the elements in its vicinity. The elements in the vicinity of the interface are defined using the interface radius ( ), which is twice or three times the greatest element diameter [7]. In Figure 1, the (light and dark) gray elements demonstrate the vicinity of the interface (the thick black line).…”

Section: Interface Advection Algorithmmentioning

confidence: 99%

“…Several stable strategies to solve the interface advection equation are proposed in the literature: Streamline Upwind Petrov-Galerkin [24] and Taylor-Galerkin [26] methods. In this research, we have employed a least-squares finite element method [7,27]. For this purpose, the domain is divided into rectangular or hexahedral subdomains or elements for 2D and 3D cases, respectively.…”

Section: Interface Advection Algorithmmentioning

confidence: 99%

“…Therefore, it is expectable that the level set function (Φ) deviates from the signed distance function. Although employing a narrow-band technique, such as the local least-square finite element method (LLSFEM) [7], prevents the excessive interface diffusion, it does not remove the demand for the re-initialization step.…”

Section: Geometrical Re-initializationmentioning

confidence: 99%

“…Fluids 2021, 6, x FOR PEER REVIEW 6 of 25 element method (LLSFEM) [7], prevents the excessive interface diffusion, it does not remove the demand for the re-initialization step. Different types of re-distancing or re-initialization are discussed in the introduction section.…”

Section: The Motivations and Preliminariesmentioning

confidence: 99%

“…Therefore, one can employ the LS values at any arbitrary time (t) to explicitly estimate the interface without applying rigorous reconstruction algorithms, as is the case for the volume of fluid (VOF) method [2][3][4][5][6]. Besides, the evaluation of the interface normal vectors and curvature values are easily attainable, owing to the smoothness of the signed distance function [7].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Improved Conservative Direct Re-Initialization Method (ICDR) for Two-Phase Flow Simulations

Mostafaiyan

Wießner

Heinrich

et al. 2021

Fluids

Self Cite

View full text Add to dashboard Cite

We introduce an improved conservative direct re-initialization (ICDR) method (for two-phase flow problems) as a new and efficient geometrical re-distancing scheme. The ICDR technique takes advantage of two mass-conserving and fast re-distancing schemes, as well as a global mass correction concept to reduce the extent of the mass loss/gain in two- and three-dimensional (2D and 3D) problems. We examine the ICDR method, at the first step, with two 2D benchmarks: the notched cylinder and the swirling flow vortex problems. To do so, we (for the first time) extensively analyze the dependency of the regenerated interface quality on both time-step and element sizes. Then, we quantitatively assess the results by employing a defined norm value, which evaluates the deviation from the exact solution. We also present a visual assessment by graphical demonstration of original and regenerated interfaces. In the next step, we investigate the performance of the ICDR in three-dimensional (3D) problems. For this purpose, we simulate drop deformation in a simple shear flow field. We describe our reason for this choice and show that, by employing the ICDR scheme, the results of our analysis comply with the existing numerical and experimental data in the literature.

show abstract

Section: Interface Advection Algorithmmentioning

confidence: 99%

Section: Interface Advection Algorithmmentioning

confidence: 99%

Section: Geometrical Re-initializationmentioning

confidence: 99%

Section: The Motivations and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Improved Conservative Direct Re-Initialization Method (ICDR) for Two-Phase Flow Simulations

Mostafaiyan

Wießner

Heinrich

et al. 2021

Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

Moving least‐squares aided finite element method: A powerful means to predict flow fields in the presence of a solid part

Mostafaiyan,

Wießner,

Heinrich

2024

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

With the assistance of the moving least‐squares (MLS) interpolation functions, a two‐dimensional finite element code is developed to consider the effects of a stationary or moving solid body in a flow domain. At the same time, the mesh or grid is independent of the shape of the solid body. We achieve this goal in two steps. In the first step, we use MLS interpolants to enhance the pressure (P) and velocity (V) shape functions. By this means, we capture different discontinuities in a flow domain. In our previous publications, we have named this technique the PVMLS method (pressure and velocity shape functions enhanced by the MLS interpolants) and described it thoroughly. In the second step, we modify the PVMLS method (the M‐PVMLS method) to consider the effect of a solid part(s) in a flow domain. To evaluate the new method's performance, we compare the results of the M‐PVMLS method with a finite element code that uses boundary‐fitted meshes.

show abstract

A LLS operator based S‐I WT de‐noising algorithm applied in EDXRF

Tang

et al. 2020

X-Ray Spectrometry

View full text Add to dashboard Cite

An improved shift‐invariant wavelet (S‐I WT) de‐noising algorithm based on LLS operator is proposed for high‐resolution energy dispersive X‐ray fluorescence. Sym8 is chosen as the wavelet basis function and performed noise reduction on the analog signal. Comparison of the de‐noising effect of S‐I WT, improved WT and LLS S‐I WT (where LLS is the log square root operator) method are quantitatively evaluated by using evaluation criteria signal‐to‐noise‐ratio (SNR), root mean square error and Pearson correlation coefficient. Meanwhile, a new evaluation criterion of de‐noising effect, called peak area relative difference, is also proposed to evaluate the counting deviation. The results show that the LLS‐SI WT is simple and reliable, can effectively reduce pseudo‐Gibbs artificial signals and statistical fluctuation. Besides, this method simplifies the calculation, reduces the running time and improves the running efficiency. The LLS‐SI WT is also applied to reduce the noise after adding strong noise to the signal, the SNR has been improved from 14.0040 to 14.7552, and most of the characteristic peak information retains to the greatest extent.

show abstract

Application of local least squares finite element method (LLSFEM) in the interface capturing of two-phase flow systems

Cited by 10 publications

References 36 publications

An Improved Conservative Direct Re-Initialization Method (ICDR) for Two-Phase Flow Simulations

An Improved Conservative Direct Re-Initialization Method (ICDR) for Two-Phase Flow Simulations

Moving least‐squares aided finite element method: A powerful means to predict flow fields in the presence of a solid part

A LLS operator based S‐I WT de‐noising algorithm applied in EDXRF

Contact Info

Product

Resources

About