Interface Reconstruction Method Research Articles

Isosurface extraction for piecewise-linear reconstruction of complex interfaces on arbitrary grids

In the field of volume of fluid type schemes, there is still great room for improvement in the accuracy of the methods used to reconstruct interfaces, especially when highly complex interfaces are involved. Isosurface extraction is exploited in a series of piecewise-linear interface reconstruction methods to simulate complex interface dynamic problems on arbitrary grids, and high-order surface patches are applied to achieve significantly improved accuracy. Isosurface extraction is also used to choose a convenient set of neighboring cells, hereafter called reconstruction stencil, for the reconstruction of highly curved interfaces when using well-known linearity-preserving methods. The relevance of the proper selection of the reconstruction stencil is highlighted, showing that the convergence of formal second-order methods can deteriorate when inappropriate reconstruction stencils are used. The accuracy, computational efficiency and performance of the implemented piecewise-linear interface reconstruction methods coupled with different reconstruction stencils are thoroughly analyzed for the reconstruction of interfaces in static conditions and dynamic simulations that produce highly deformed interfaces by using an accurate unsplit geometric advection method and imposing prescribed velocity fields.

An analytic approach for the moment-of-fluid interface reconstruction method on tetrahedral meshes

This article presents an original fast and robust approach for solving the moment-of-fluid interface reconstruction problem on tetrahedral meshes. We establish an explicit parametrization of the locus of the centroids under volume constrains using the spherical coordinates on a reference tetrahedron. This parametrization allows to write the moment-of-fluid objective function and its gradient by means of analytic formulas. Then, we show that the minimization problem on arbitrary tetrahedra can be effectively solved on the reference tetrahedron by using an affine transformation. Based on this transformation, we propose a improved technique for obtaining an initial condition for the minimization algorithm. We then describe the Gauss-Newton and the BFGS minimization algorithms, both combined with a trust-region method, to solve this reconstruction problem. Finally, we perform a verification and validation process on a series of increasingly complex test cases. These tests show that the proposed analytic method, paired with the Gauss-Newton algorithm, outperforms the other methods that were tested.

An adaptive moments-based interface reconstruction using intersection of the cell with one half-plane, two half-planes and a circle

We present a new adaptive moment-of-fluid (A-MOF) interface reconstruction method. It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to construct a shape that approximates the respective material fragment. The new method requires information about the material moments only for the cell under consideration. The adaptive method chooses between shapes obtained by the intersection of the cell with one half-plane, two half-planes, or a circle. The A-MOF method allows to exactly reproduce several convex shapes: corners, filaments, and their concave cell-complements; as well as pieces of the circles and its cell-compliments. Interface reconstruction is formulated as a local (for each cell), non-linear, equality constrained optimization problem, which does not require additional communication and allows for an efficient parallel implementation.We present an extensive set of test problems, both for interface reconstruction on a single cell, and for reconstruction of a variety of shapes on the entire mesh.

A two‐dimensional multimaterial ALE method for compressible flows using coupled volume of fluid and level set interface reconstruction

AbstractIn this work, we present a two‐dimensional multimaterial arbitrary Lagrangian–Eulerian (ALE) method for simulating compressible flows in which a novel coupled volume of fluid and level set interface reconstruction (VOSET) method is developed for interface capturing. The VOSET method combines the merits of both the volume of fluid method and the level set method by using a geometrical iterative operation. Compared to the original VOSET method, the novel VOSET method proposed in this work further improves the accuracy and fidelity in interface reconstruction procedure, especially in under‐resolved regions. Several typical two‐dimensional numerical experiments are presented to investigate the effectiveness of the proposed VOSET method and its performance when coupling with the multimaterial ALE solver. Numerical results demonstrate its good capability in capturing material interfaces during the simulation of compressible two‐material flows.

A horizontal refined piecewise linear interface reconstruction (HOPLIRE) method based on the VOSET method for capturing the two-phase interface

The interface reconstruction method is significant for the numerical research of the two-phase problem, but the implementation of popular ones is not easy enough. In this paper, a horizontal refined piecewise linear interface reconstruction (HOPLIRE) method with a straightforward implementation procedure is proposed for the incompressible flow, and the idea of that is to reconstruct the two-phase interface in one grid cell with many horizontal refined pieces. Only one situation without complex classifications needs to be considered for reconstructing the interface, and the volume fraction flux through the grid cell face can be easily obtained to solve the VOF function by a simple four fundamental operations of arithmetic. In addition to the advantages of simple implementation for the HOPLIRE method, the accuracy of the reconstructed vapor–liquid interface is also high. The proximity between the HOPLIRE method and the popular piecewise linear interface reconstruction (PLIC) method increases with the divided piece number of the HOPLIRE method, and 30 is recommended based on calculation accuracies of LS function, interface direction, and curvature. Besides, the good performances of the VOSET-HOPLIRE method in the calculation accuracy and efficiency are verified by comparing with VOF-PLIC and VOSET-PLIC methods by some classical two-phase problems. Currently, the HOPLIRE method is only presented based on a two-dimensional problem under a structured mesh. In the future, this methodology will be improved to cover three-dimensional problems and unstructured meshes.

Numerical analysis on subcooled boiling in PWR coolant channel based on a modified multi-scale interface model

A modified multi-scale interface model was employed with the Eulerian two-fluid framework to investigate the three-dimensional characteristics of subcooled boiling characteristics in a typical Pressurized Water Reactor (PWR) coolant channel with mixing grid. Based on the morphology identification by adopting an advanced interface topology map, the phase-average method and the interface-reconstruction method can be applied for dispersed bubble and sharp interface, respectively, to improve the calculated precision of interfacial transfers. Models were validated by using the dam break data for sharp interface topology and employing the flow boiling experimental data for the phase distribution in both radial and axial directions. The calculated results agreed well with the experimental data. Thermohydraulic characteristics in the coolant channel were obtained, including void fraction, phase velocity and flow streamline, based on which, the effects of mixing vane on the localized field were analyzed. The vapor volume fraction was decreased in downstream of spacer grid due to the mixing effect, while the lateral flow was enhanced. The vapor accumulation phenomenon was captured and the sharp interface between the liquid and the accumulated vapor was identified by the modified model. Based on this, the interfacial transfer characteristics of the sharp interface was considered in simulations.

Numerical study of drop impact on slippery lubricated surfaces

We numerically study drop impact on slippery lubricated surfaces at varied impact speeds to comprehend the cloaking of the water drop by the lubricant. We employ a multi-material and multi-phase interface reconstruction method to capture the interaction between the drop and the lubricants of varying interfacial tensions. We demonstrate that cloaking occurs when lubricant water interfacial tensions are low and impact speeds are low. Our research demonstrates that the thickness of the encapsulating lubricant layer varies over time. At moderate impact speeds of 0.25 and 0.5 m/s, the drop displaces a large amount of lubricant, generating a lubricant–water jet, as we also demonstrate. At high impact speeds of 5 and 30 m/s, a secondary impingement forms, which displaces a significant amount of lubricant to reveal the underneath substrate that was not visible at lower impact speeds. Finally, we investigate the drop impact on lubricant infused micro-wells with varying spacing. We find that small spacing between the micro-well walls can limit lubricant drainage and displacement. The substrates with micro-wells exhibit far less splashing than those without. Furthermore, we demonstrate that micro-wells are better at preserving lubricants than substrates without micro-wells.

Moments-based interface reconstruction, remap and advection

We present a new moment-of-fluid (MOF2) interface reconstruction method. It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to reconstruct a convex material polygon or a union of convex polygons that approximate the respective material fragment. The new method requires information about the material moments only for the cell under consideration. The MOF2 method allows to exactly reproduce several convex shapes: corners, filaments, and some concave shapes: cell-complements to corners and filaments.Interface reconstruction is formulated as a local (for each cell), non-linear, equality constrained optimization problem, which does not require additional communication and allows for an efficient parallel implementation.We present an extensive set of test problems, both for interface reconstruction on a single cell, and for reconstruction of a variety of shapes on a variety of meshes.We describe how to perform two-material advection using the MOF2 method and present the results for the classical advection tests.We also show the examples of material interface remapping needed in the framework of multi-material arbitrary Lagrangian-Eulerian methods, and give a brief description of a procedure that can be used to update the material moments on the Lagrangian stage of those methods.

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

In this paper, we propose an adaptive mesh refinement method for 2D multi-material compressible non-viscous flows in semi-Lagrangian coordinates.The mesh adaptation procedure is local and relies on a discrete metric field evaluation. The remapping method is second-order accurate and we prove its stability. We propose a multi-material treatment using two ingredients: the local remeshing is performed in a way that reduces as much as possible the creation of mixed cells and an interface reconstruction method that can be used to avoid the diffusion of the material interfaces.The obtained method is almost Lagrangian and can be implemented in a parallel framework. We provide some numerical tests which attest the validity of the method and its robustness.

GVOF: An open-source package for unsplit geometric volume of fluid methods on arbitrary grids

The gVOF package implements several accurate and efficient geometric volume of fluid (VOF) methods on arbitrary grids, either structured or unstructured with convex or non-convex cells, based on multidimensional unsplit advection and piecewise linear interface calculation (PLIC) schemes, with the purpose of facilitating and extending the use of advanced unsplit geometric VOF methods in new or existing computational fluid dynamics codes. The package includes a complete and self-contained set of routines for VOF initialization, interface reconstruction and fluid advection, and uses as external libraries a set of publicly available in-house tools to perform several analytical and geometrical operations. These operations may involve handling of high-complex non-convex flux polyhedra, even with self-intersecting faces, which are robustly and efficiently treated in this work without the need of costly techniques based on convex decomposition. Results for the accuracy, computational efficiency, and volume (local and global) conservation properties of different combinations of the implemented advection and reconstruction methods are presented for several numerical tests on structured and unstructured grids. An extensive comparison with results obtained by other authors using advanced geometric VOF methods shows the outstanding performance of the gVOF package in terms of efficiency and accuracy. To demonstrate the performance of the package in solving complex two-phase flow problems, the implemented methods are combined with an existing in-house code to simulate the impact of a water drop on a free surface. Program summaryProgram Title:gVOFCPC Library link to program files:https://doi.org/10.17632/9gmn6gsb6p.1Licensing provisions: GPLv3Programming language:FORTRAN and C, with C interfacesExternal routines/libraries:VOFTools (https://doi.org/10.17632/brrgt645bh.3) and isoap (https://doi.org/10.17632/4rcf98s74c.1) librariesNature of problem: The software package includes efficient and accurate routines for volume of fluid initialization, reconstruction of interfaces and fluid advection on arbitrary grids, either structured or unstructured with convex or non-convex cells, which are used to implement advanced unsplit geometric VOF methods. In particular, the package includes a fluid volume fraction initialization method, six PLIC reconstruction methods and three multidimensional unsplit advection methods. Routines to visualize interfaces and compute reconstruction errors; tests to assess the accuracy, computational efficiency, and volume conservation of the implemented methods for the reconstruction and advection of complex interfaces on arbitrary grids; and a user manual have also been included in the supplied package.Solution method: Basically, the implemented methods, which can be used on grids with polyhedral cells of arbitrary geometry, have the following general characteristics. The methods implemented for fluid volume fraction initialization and reconstruction error calculation are based on a recursive grid refinement procedure to compute the fluid volume bounded by cell edges and an implicitly-defined fluid interface. The six implemented interface reconstruction methods are the following: a least-squares gradient interface reconstruction method; three isosurface-based interface reconstruction methods; an extension to 3D of the iterative Swartz interface reconstruction; and a least-squares fit interface reconstruction method. Three unsplit advection methods, which are based on edge-matched, face-matched and non-matched flux polyhedra and are valid for 3D arbitrary grids, are implemented. All the implemented methods can be combined by the user to solve different tests on arbitrary grids. The implemented routines can be used in FORTRAN or C. The OpenMP application programming interface is used to improve the computational efficiency.

Electrochemical interface reconstruction to eliminate surface heterogeneity for dendrite-free zinc anodes

Metallic zinc anodes have attracted growing interest for aqueous rechargeable batteries owing to their high theoretical capacity and low cost. However, the practical application of zinc anodes is limited by the low Coulombic efficiency resulted from the irrepressible dendrite growth. Herein, we prove that the dendrite formation under low current density is mainly controlled by the surface heterogeneity. According to this fundamental principle, a facile electrochemical interface reconstruction method is proposed to uniformize zinc deposition and dissolution by initial electrostripping activation under high current density, which can effectively eliminate the influence of surface heterogeneity. The reconstructed zinc anode shows highly reversible stripping/plating behavior and significantly enhanced cycling stability in both symmetric and full cells. Moreover, the zinc-ion hybrid capacitor can steady operate for 8000 cycles with 96% capacity retention after one-step electrochemical reconstruction at an optimal current density based on its rapid charging-discharging ability

Three-dimensional cellwise conservative unsplit geometric VOF schemes

This work presents two unsplit geometric VOF schemes that extend the two-dimensional cellwise conservative unsplit (CCU) scheme (Comminal et al. (2015) [49]) to three dimensions. The novelty of the 3D-CCU schemes lies in the representation of the streaksurfaces of donating regions by polyhedral surfaces whose vertices are calculated with the 4th order Runge-Kutta scheme. Moreover, the advected liquid volumes are computed using a truncation algorithm (López et al. (2019) [62]) suited for arbitrary non-convex and self-intersecting polyhedra, which removes the need for tetrahedral decomposition. The 3D-CCU advection schemes were coupled to three interface reconstruction methods (Youngs' method, the Mixed Youngs-Centered scheme, and the Least-Square Fit algorithm). The resulting VOF methods were tested in classical benchmark advection tests, including translation, rigid-body rotation, shear and deformation flows. The proposed 3D-CCU schemes conserve the liquid volume and maintain the physical boundedness of liquid volume fractions to the machine precision. The 3D-CCU schemes perform favorably compared to other unsplit geometric VOF schemes when coupled to Youngs' interface reconstruction method. Moreover, the 3D-CCU schemes coupled to the Least-Square Fit algorithm are more accurate than most other VOF schemes that use a second-order accurate interface reconstruction, except those where a 3D extension of the Mosso-Swartz interface reconstruction is employed. The comparison of the different VOF schemes highlights the importance of coupling accurate interface reconstruction methods with accurate unsplit advection schemes.

An improved continuity-preserving interface reconstruction method for multi-material flow

The dynamic programming interface reconstruction (DPIR) method introduced by Dumas et al.[1] is a volume-preserving and continuous interface reconstruction method. It is a two-step method, which comprises of an optimized step and a correction step. At first, in the optimized step, it minimizes a target function by the dynamic programming method to obtain a continuous interface. Then, it corrects the interface in each mixed cell to preserve the conservative of the volume fraction. However, only the difference of volume fraction is considered, and the interface normal is neglected in the target function. These make it easy to obtain different optimal results in the optimized step, and hence the resulting continuous interfaces always suffer from oscillations (i.e., the ‘wave effects’ [1]). In this paper, to suppress the continuous interfaces’ oscillations in the optimized step and improve its accuracy, we constructed a non-dimensional target function based on the moment-of-fluid method’s objective function, and also proposed a new correction method. Finally, several numerical tests are performed to show the new method’s superiority over the original one of Dumas et al. [1].

Analytic gradient for the moment-of-fluid method in axisymmetric and on general polyhedrons in any dimension

The moment-of-fluid method (MOF) is an interface reconstruction method similar to the volume-of-fluid method with piecewise linear interface reconstruction (VOF-PLIC). In the MOF method, the normal to the interface is found by minimizing the distance between the centroid of the polyhedron below the interface and a reference centroid under a volume constraint. To solve this minimization problem, the gradient of the objective function must be evaluated. Analytic formulas have been proposed by many authors to compute the gradient in 2D on general polygons with a polar parametrization and in 3D on convex polyhedrons with a spherical parametrization. In this short note, we propose a more general formula that covers non-convex polyhedrons in any dimension and axisymmetric coordinates. Furthermore, this formula does not depend on the parametrization of the normal to the interface. We also provide some practical way to use the formula in a code.

An accurate interface reconstruction method using piecewise circular arcs

SummaryA novel piecewise circular interface construction (PCIC) method for accurate reconstruction of interface in a two‐phase flow problem is proposed. This is under the framework of a fixed grid, volume of fluid approach applied on a two‐dimensional semistaggered structured grid. Fluid interface in each mixed cell is represented using a geometric template of piecewise circular arc. Data corresponding to arc center coordinates and radius are first predicted using curve fitting methods and corrected with the help of volume fraction constraints. Further corrections are carried out to achieve function (c0) continuity at cell boundaries. The proposed method does not require additional calculations for the determination of curvature (for calculation of surface tension force), since it is obtained as part of reconstruction process itself. For dynamic interface construction, simple analytical expressions are derived to construct edge matched flux polygons. Area of intersection of flux polygons with area covered by primary fluid is determined to effect geometric advection across a PCIC interface. Accuracy of this method is demonstrated by the reconstruction of standard static and dynamically evolving interface problems. Accuracy levels superior to most interface reconstruction methods using PLIC and schemes using higher order curves are established. Finally, the capability to handle a complex two‐phase flow problem simulation viz the four‐vortex flow field, where interface undergoes breakage and coalescence, is also demonstrated.

A Fast Interface Reconstruction Method for Frequency-Domain Synthetic Aperture Focusing Technique Imaging of Two-Layered Systems with Non-planar Interface Based on Virtual Points Measuring

Frequency-domain synthetic aperture focusing technique (SAFT), such as non-stationary phase shift migration (NSPSM), plays an essential role in the ultrasonic imaging of two-layered systems with non-planar interfaces. However, with NSPSM fast imaging under blind test conditions is hard to realize due to a lack of interface information in practice. To overcome this difficulty, a fast interface reconstruction method for NSPSM imaging of non-planar two-layered systems is proposed based on virtual points measuring. In blind testing conditions, a series of virtual points (VP) were created at the non-planar interface of the two-layered system by the time-of-flight (TOF) of the first incoming echo. Then, the interface for the two-layered system was quickly established by the interpolation of the VP. Finally, the NSPSM imaging for the two-layered system with non-planar interfaces was realized by the borderline which is used to distinguish the velocities of the coupling medium and tested part in the same extrapolating depth. The imaging results showed that the position of side-drilled holes was located correctly and the efficiency of the algorithm was significantly improved. Hence, the VP-NSPSM method is expected to achieve fast or even real-time imaging of two-layered systems with non-planar interfaces in practical NDT applications.

Moment-of-fluid analytic reconstruction on 3D rectangular hexahedrons

The moment-of-fluid method (MOF) is a second-order accurate interface reconstruction method which can be seen as an extension of the volume-of-fluid method with piecewise linear interface construction (VOF-PLIC). MOF involves a computationally intensive minimization problem that needs to be solved on every cell containing several materials. We propose a new fast and robust reconstruction algorithm to tackle this problem on rectangular hexahedral cells. Our approach uses explicit analytic formulas of the objective function that does not use any geometric computations such as half-space–polyhedron intersections. The numerical results show that the proposed method is more robust and more than 200 times faster than the original approach. Additionally, we propose a faster reconstruction algorithm on convex polyhedral cells. All the methods presented in this article have been implemented and verified on the open-source code Notus.

Curved interface reconstruction for 2D compressible multi-material flows

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR [1], which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to unstructured grid. Finally, we describe an extension to three materials.

A 3D Moment of Fluid method for simulating complex turbulent multiphase flows

This paper presents the moment of fluid method as a liquid/gas interface reconstruction method coupled with a mass momentum conservative approach within the context of numerical simulations of incompressible two-phase flows. This method tracks both liquid volume fraction and phase centroid for reconstructing the interface. The interface reconstruction is performed in a volume (and mass) conservative manner and accuracy of orientation of interface is ensured by minimizing the centroid distance between original and reconstructed interface. With two-phase flows, moment of fluid method is able to reconstruct interface without needing phase volume data from neighboring cells. The performance of this method is analyzed through various transport and deformation tests, and through simple two-phase flows tests that encounter changes in the interface topologies. Exhaustive mesh convergence study for the reconstruction error has been performed through various transport and deformation tests involving simple two-phase flows. It is then applied to simulate atomization of turbulent liquid diesel jet injected into a quiescent environment. The volume conservation error for the moment of fluid method remains small for this complex turbulent case.

A coupled MMALE-FE method for solving 3D fluid-solid interaction problems with multi-material flow

Purpose The simulation of the fluid–solid interaction (FSI) problem is important for both academic studies and engineering applications. However, the numerical approach for simulating the FSI problems is a great challenge owing to the large discrepancy of material properties and inconsistent description of grid motion between the fluid and solid domains. The difficulties will be further increased if there are multiple materials in the fluid region. In these complicated applications, interface reconstruction, multi-material advection and FSI must be all taken into account. This paper aims to present an effective integrated work of multi-material arbitrary Lagrangian Eulerian (MMALE) method, finite element (FE) method and the continuum analogy method to simulate the complex FSI problems involving multi-material flow. The coupled method is used to simulate the three-dimensional CONT test and the blast-plate interaction. The numerical results show good agreement with the benchmark and the experiment data, which indicates that the presented method is effective for solving the complicated FSI problems. Design/methodology/approach MMALE and FE methods are used to simulate fluid and solid regions, respectively. The interfacial nodes of fluid and solid are required to be coincident in the whole simulation so the interacted force can be easily and accurately calculated. To this end, the continuum analogy method is used in the rezoning phase. Findings The coupled method is used to simulate the three-dimensional CONT test and the blast-plate interaction. The numerical results show good agreement with the benchmark and the experiment data, which indicates that the presented method is effective for solving the complicated FSI problems. Originality/value To the best of the authors’ knowledge, this is the first time that the ALE method, moment of fluid interface reconstruction method, continuum analogy method and the FE method are combined to solve complicated practical problems.