A Comparative Study of Interpolation Schemes in Overset Meshes for the PLIC-VOF Method in Multiphase Flows

2020 ◽  
Author(s):  
Yanni Chang ◽  
Dezhi Dai ◽  
Albert Y. Tong
Keyword(s):  
Multiphase Flows ◽  
Piecewise Linear ◽  
Rotational Velocity ◽  
Weighted Average ◽  
Vof Method ◽  
Test Cases ◽  
Interpolation Scheme ◽  
Interface Capturing ◽  
Different Shapes ◽  
Geometric Interpolation

Abstract Piecewise Linear Interface Calculation (PLIC) schemes have been extensively employed in the Volume-of-Fluid (VOF) method for interface capturing in numerical simulations of multiphase flows. Dynamic overset meshes can be especially useful in applications involving component motions and complex geometric shapes. The basic idea of the overset mesh is the variable field interpolation within the overlapped region between the background and body meshes. The acceptor cell value is evaluated by a weighted average of its donors. The weighting factors are calculated by different algebraic methods, such as the averageValue, injection and inverseDistance schemes, which are implanted in the foam-extend library. A geometric interpolation scheme of the VOF field in overset meshes for the PLIC-VOF method has been proposed in the present study. The VOF value of an acceptor cell is evaluated geometrically with the reconstructed interfaces from the corresponding donor elements. Test cases of advecting liquid columns of different shapes inside a unit square/cube with a prescribed rotational velocity field have been performed to demonstrate the accuracy of the proposed overset interpolation scheme by comparing it with three algebraic ones. The proposed scheme has been shown to yield higher accuracy.

scholarly journals Modified Predictor-Corrector WAF Method for the Shallow Water Equations with Source Terms

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Montri Maleewong
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Piecewise Linear ◽  
Weighted Average ◽  
Test Cases ◽  
Half Time ◽  
Source Terms ◽  
Time Step ◽  
Predictor Corrector

A modified predictor-corrector scheme combining with the depth gradient method (DGM) and the weighted average flux (WAF) method has been presented to solve the one-dimensional shallow water equations with source terms. Approximate solutions in the predictor step are obtained by the DGM with piecewise-linear reconstructions in each cell volume. The source terms can then be calculated directly by these predicted values at the corresponding half-time step. In the corrector step, the TVD version of the WAF method is applied to calculate the numerical fluxes at the same half-time step for each cell face. The accuracy of numerical solutions is shown by applying the method to solve various test cases in both steady and unsteady problems with and without source terms. It shows that the numerical results are in good agreement with the existing analytical solutions as well as experimental data in some test cases.

Simulation of Dendritic Growth Using a VOF Method

2009 ◽  
Author(s):  
Joaqui´n Lo´pez ◽  
Julio Herna´ndez ◽  
Claudio Zanzi ◽  
Fe´lix Faura ◽  
Pablo Go´mez
Keyword(s):  
Dendritic Growth ◽  
Piecewise Linear ◽  
Height Function ◽  
Vof Method ◽  
Three Dimensions ◽  
Advection Equation ◽  
Thermal Gradients ◽  
Interfacial Flows ◽  
Thermal Boundary Conditions ◽  
Interface Curvature

The volume of fluid (VOF) method is one of the most widely used methods to simulate interfacial flows using fixed grids. However, its application to phase change processes in solidification problems is relatively infrequent. In this work, preliminary results of the application of a new methodology to the simulation of dendritic growth of pure metals is presented. The proposed approach is based on a recent VOF method with PLIC (piecewise linear interface calculation) reconstruction of the interface. A diffused-interface method is used to solve the energy equation, which avoids the need of applying the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to accurately obtain the front velocity, are calculated with the aid of a distance function. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by Lo´pez et al. [J. Comput. Phys. 195 (2004) 718–742] (extended to three dimensions by Herna´ndez et al. [Int. J. Numer. Methods Fluids 58 (2008) 897-921]). The interface curvature is computed using an improved height function (HF) technique, which provides second-order accuracy. The assessment of the proposed methodology is carried out by comparing the numerical results with analytical solutions and with results obtained by different authors for the formation of complex dendritic structures in two and three dimensions.

An Improved High-Resolution Discretization Scheme for Volume-of-Fluid CFD Simulations

2007 ◽  
Author(s):  
D. Keith Walters ◽  
Nicole M. Wolgemuth
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Volume Fraction ◽  
Phase Interface ◽  
Volume Of Fluid ◽  
Volume Control ◽  
Test Cases ◽  
Discretization Scheme ◽  
Spatial Discretization ◽  
Interface Capturing

A new high-resolution spatial discretization scheme for use with the interface capturing volume-of-fluid (VOF) method is presented and applied to several test cases. The new scheme is shown to preserve the volume fraction discontinuity within a single computational control volume (CV), without the need to explicitly reconstruct the interface within CVs near the interface. The method is based on maximization of the volume fraction gradient in the region of the interface, while stability is preserved by maintaining net upwind biasing of the face flux prescription in each CV. In addition, the scheme employs face limiting to satisfy physical boundedness criteria at finite-volume control surfaces (faces) and prevent variable overshoot. The method has been developed for use with unstructured, anisotropic, and/or inhomogeneous meshes that are often used for simulation of geometrically complex flowfields. This paper presents the implementation of the new discretization scheme into a steady-state solver in order to isolate the spatial discretization from the time integration technique. The new scheme is validated for steady-state two-phase flow using several demonstration test cases, and is shown to preserve the phase interface almost exactly, with essentially zero dissipative or dispersive error in the volume fraction solution. Results are compared to existing 2nd order and high-resolution interface capturing (HRIC) schemes, and shown to be superior in all cases.

Assessment of Enhanced Multi-Dimensional Limiting Process for Multi-Dimensional Flows

2011 ◽  
Author(s):  
Kyu Hong Kim ◽  
Jung Ho Park
Keyword(s):  
Higher Order ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Interpolation Scheme ◽  
Local Extrema ◽  
Numerous Test ◽  
High Order Interpolation

In this paper, a new limiting process based on the Multi-dimensional Limiting Process, called enhanced Multi-dimensional Limiting Process is developed and tested with several cases. The enhanced Multi-dimensional Limiting Process, e-MLP has a number of useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. The new limiting process was applied to numerous test cases. Through these tests, we could confirm that e-MLP enhances the accuracy and efficiency with both continuous and discontinuous multidimensional flows.

Study on the Computation Method of Bilinear System With Piecewise Damping

2006 ◽  
Author(s):  
Qiwei He ◽  
Shijian Zhu ◽  
Jingjun Lou
Keyword(s):  
Linear System ◽  
Integration Method ◽  
Piecewise Linear ◽  
Critical Time ◽  
Bilinear System ◽  
Computation Method ◽  
Direct Integration ◽  
Interpolation Scheme ◽  
Piecewise Linear System ◽  
Direct Integration Method

An "inverse" integration method to solve the piecewise linear system numerically is discussed. A bilinear system with piecewise damping is calculated using this method and compared with the results using interpolation scheme and direct integration method. Taking the displacement and the contact force as integration variables, the "inverse" integration method can evaluate the critical time when the non-smoothness occurs more precisely than other direct integration method and interpolation scheme.

Computations of Single and Multiphase Flows Using a Lattice Boltzmann Solver

2019 ◽  
Author(s):  
M. Wasy Akhtar ◽  
Holley C. Love
Keyword(s):  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Single Phase ◽  
Incompressible Flows ◽  
Navier Stokes ◽  
Advection Equation ◽  
Test Cases ◽  
Collision Term ◽  
Multiphase Model ◽  
Advection Term

Abstract There is considerable interest in high fidelity simulation of both single phase incompressible flows and multiphase flows. Most commonly applied numerical methods include finite difference, finite volume, finite element and spectral methods. All of these methods attempt to capture the flow details by solving the Navier–Stokes equations. Challenges of solving the Navier–Stokes single phase incompressible flows include the non-locality of the pressure gradient, non-linearity of the advection term and handling the pressure-velocity coupling. Multiphase flow computations pose additional challenges, such as property and flow variable discontinuities at the interface, whose location and orientation is not known a priori. Further, capturing/tracking of the multiphase interface requires solution of an additional advection equation. Recently, the lattice Boltzmann method has been applied to compute fluid dynamics simulations both for single and multiphase configurations; it is considered a modern CFD approach with improved accuracy and performance. Specifically, we employ a multiple-relaxation time (MRT) technique for the collision term on a D3Q27 lattice. The multiphase interface is captured using the phase-field approach of Allen-Cahn. Test cases include lid driven cavity, vortex shedding for a double backward facing step, Rayleigh Taylor instability, Enright’s deformation test and rising bubble in an infinite domain. These test cases validate different aspects of the single and multiphase model, so that the results can be interpreted with confidence that the underlying computational framework is sufficiently accurate.

Numerical Analysis of Wave Impact Loads on Semi-Submersible Platform

2017 ◽  
Author(s):  
Kangping Liao ◽  
Wenyang Duan ◽  
QingWei Ma ◽  
Shan Ma ◽  
Binbin Zhao ◽  
...  
Keyword(s):  
Numerical Method ◽  
Structural Damage ◽  
Fluid Model ◽  
Test Cases ◽  
Impact Loads ◽  
Extreme Wave ◽  
Wave Impact ◽  
Interface Capturing ◽  
Volume Of Fluid Model ◽  
Rough Sea

In rough sea conditions, semi-submersible platform often suffers from extreme wave impact loads, which can result in structural damage. It is important to predict the wave impact loads on semi-submersible platform. Therefore, the purpose of this study is to investigate the wave impact loads on semi-submersible platform with numerical methods. A numerical method, based on a fixed regular Cartesian grid system, has been developed by the authors. In the method, the FDM (Finite Difference Method) is applied for solving flow field, and the THINC/SW (Tangent of Hyperbola for INterface Capturing with Slope Weighting) model, which is kind of VOF (Volume-of-Fluid) model, is adopted to capture the free surface. Some selected model test cases, form Exwave JIP project, will be used to validate the present numerical method and to analyze the wave impact loads on semi-submersible platform.

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