An accurate interface reconstruction method using piecewise circular arcs

A 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.     

Effects of element order and interface reconstruction in FEM/volume‐of‐fluid incompressible flow simulation

In previous studies, the moment‐of‐fluid interface reconstruction method showed dramatic accuracy improvements in static and pure advection tests over existing methods, but this did not translate into an equivalent improvement in volume‐tracked multimaterial incompressible flow simulation using low‐order finite elements. In this work, the combined effects of the spatial discretization and interface reconstruction in flow simulation are examined. The mixed finite element pairs, Q₁Q₀ (with pressure stabilization) and Q₂P _{? 1} are compared. Material order‐dependent and material order‐independent first and second‐order accurate interface reconstruction methods are used. The Q₂P _{? 1} elements show significant improvements in computed flow solution accuracy for single material flows but show reduced convergence using element‐average piecewise constant density and viscosity in volume‐tracked simulations. In general, a refined Q₁Q₀ grid, with better material interface resolution, provided an accuracy similar to the Q₂P _{? 1} element grid with a comparable number of degrees of freedom. Moment‐of‐fluid shows more benefit from the higher‐order accurate flow simulation than the LVIRA, Youngs', and power diagram interface reconstruction methods, especially on unstructured grids, but does not recover the dramatic accuracy improvements it has shown in advection tests. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Adaptive subdivision piecewise linear interface calculation (ASPLIC) for 2D multi‐material hydrodynamic simulation codes

In this work, we propose an adaptive subdivision piecewise linear interface calculation (PLIC) for 2D multimaterial hydrodynamic simulation codes. Classical volume‐of‐fluid PLIC technique uses one line segment and one given normal to separate two materials. Unfortunately, these paradigms are not sufficient when filaments occur, leading to the creation of flotsam and jetsam. We propose to detect such situations and to split the computational mixed cell into reconstruction subzones. Within these subzones, one computes a so‐called subgradient using an incomplete stencil of neighbors, and the material is distributed in these subzones. Given subzone volume fraction and the subgradient, one computes one line segment using classical PLIC method, leading to a modified PLIC method for subscale material entity. The subdivision procedure relies on a splitting point, which is chosen as a specific information about the relative location of the filament in the cell, leading to an adaptive subdivision for PLIC reconstructions. Numerical tests are carried out in a 2D Lagrange + Remap multimaterial hydrodynamics Eulerian code. Static and dynamic filaments and fragments are simulated in advection or stretched in vortex‐like motion. The full hydrodynamics equations are solved on a more realistic test (shock‐bubble impact). Results show that our approach supplements classical PLIC method for situations when filaments and fragments occur. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical errors of the volume‐of‐fluid interface tracking algorithm

One of the important limitations of the interface tracking algorithms is that they can be used only as long as the local computational grid density allows surface tracking. In a dispersed flow, where the dimensions of the particular fluid parts are comparable or smaller than the grid spacing, several numerical and reconstruction errors become considerable. In this paper the analysis of the interface tracking errors is performed for the volume‐of‐fluid method with the least squares volume of fluid interface reconstruction algorithm. A few simple two‐fluid benchmarks are proposed for the investigation of the interface tracking grid dependence. The expression based on the gradient of the volume fraction variable is introduced for the estimation of the reconstruction correctness and can be used for the activation of an adaptive mesh refinement algorithm. Copyright © 2002 John Wiley & Sons, Ltd.     

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

A new interface reconstruction method in 3D is presented. The method involves a conservative level‐contour reconstruction coupled to a cubic‐Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second‐order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required. Copyright © 2008 John Wiley & Sons, Ltd.     

Portable data‐parallel surface reconstruction on a uniform rectilinear grid

With the increasing heterogeneity and on‐node parallelism of high‐performance computing hardware, a major challenge is to develop portable and efficient algorithms and software. In this work, we present our implementation of a portable code to perform surface reconstruction using NVIDIA's Thrust library. Surface reconstruction is a technique commonly used in volume tracking methods for simulations of multimaterial flow with interfaces. We have designed a 3D mesh data structure that is easily mapped to the 1D vectors used by Thrust and at the same time is simple to use and uses familiar data structure terminology (such as cells, faces, vertices, and edges). With this new data structure in place, we have implemented a piecewise linear interface reconstruction algorithm in 3 dimensions that effectively exploits the symmetry present in a uniform rectilinear computational cell. Finally, we report performance results, which show that a single implementation of these algorithms can be compiled to multiple backends (specifically, multi‐core CPUs, NVIDIA GPUs, and Intel Xeon Phi processors), making efficient use of the available parallelism on each. We also compare performance of our implementation to a legacy FORTRAN implementation in Message Passing Interface (MPI) and show performance parity on single and multi‐core CPU and achieved good parallel speed‐ups on GPU. Our research demonstrates the advantage of performance portability of the underlying data‐parallel programming model.     

Multi‐material incompressible flow simulation using the moment‐of‐fluid method

This paper compares the numerical performance of the moment‐of‐fluid (MOF) interface reconstruction technique with Youngs, LVIRA, power diagram (PD), and Swartz interface reconstruction techniques in the context of a volume‐of‐fluid (VOF) based finite element projection method for the numerical simulation of variable‐density incompressible viscous flows. In pure advection tests with multiple materials MOF shows dramatic improvements in accuracy compared with the other methods. In incompressible flows where density differences determine the flow evolution, all the methods perform similarly for two material flows on structured grids. On unstructured grids, the second‐order MOF, LVIRA, and Swartz methods perform similarly and show improvement over the first‐order Youngs' and PD methods. For flow simulations with more than two materials, MOF shows increased accuracy in interface positions on coarse meshes. In most cases, the convergence and accuracy of the computed flow solution was not strongly affected by interface reconstruction method. Published in 2009 by John Wiley & Sons, Ltd.     

From level set to volume of fluid and back again at second‐order accuracy

We present methods for computing either the level set function or volume fraction field from the other at second‐order accuracy. Both algorithms are optimal in that O(N) computations are needed for N total grid points and both algorithms are easily parallelized. This work includes a novel interface reconstruction algorithm in three dimensions that requires a smaller local block of volume fractions than existing algorithms. A compact local solver leads to better algorithm portability and efficiency: for example, fewer restrictions must be imposed on an adaptive mesh, and fewer grid cells must be communicated between processors in a parallel implementation. We also present a fast sweeping method for computing a unique approximation of the signed distance function to a piecewise linear interface. All of the numerical examples confirm second‐order accuracy on both uniform and tree‐based adaptive grids. Copyright © 2015 John Wiley & Sons, Ltd.     

A new volume of fluid method in three dimensions—Part I: Multidimensional advection method with face‐matched flux polyhedra

A multidimensional advection scheme in 3D based on the use of face‐matched flux polyhedra to integrate the volume fraction evolution equation is proposed. The algorithm tends to reduce the formation of ‘over/undershoots’ by alleviating the over/underlapping of flux polyhedra, thus diminishing the need to use local redistribution algorithms. The accuracy and efficiency of the proposed advection algorithm, which are analyzed using different tests with prescribed velocity field, compare well with other multidimensional advection methods proposed recently. The algorithm is also applied, in combination with a Navier–Stokes solver, to reproduce the impact of a water droplet falling through air on a pool of deep water. The interfacial curvature is calculated using a height‐function technique with adaptive stencil adjustment, which provides improved accuracy in regions of low grid resolution. The comparison of the numerical results with experimental results shows a good degree of agreement. Copyright © 2008 John Wiley & Sons, Ltd.     

Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids

A new adaptive quadtree method for simulating laminar viscous fluid problems with free surfaces and interfaces is presented in this paper. The Navier–Stokes equations are solved with a SIMPLE‐type scheme coupled with the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) (Numerical prediction of two fluid systems with sharp interfaces, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1997) volume of fluid (VoF) method and PLIC reconstruction of the volume fraction field during refinement and derefinement processes. The method is demonstrated for interface advection cases in translating and shearing flow fields and found to provide high interface resolution at low computational cost. The new method is also applied to simulation of the collapse of a water column and the results are in excellent agreement with other published data. The quadtree grids adapt to follow the movement of the free surface, whilst maintaining a band of the smallest cells surrounding the surface. The calculation is made on uniform and adapting quadtree grids and the accuracy of the quadtree calculation is shown to be the same as that made on the equivalent uniform grid. Copyright © 2004 John Wiley & Sons, Ltd.     

A new volume‐preserving and continuous interface reconstruction method for 2D multi‐material flow

A new two‐dimensional interface reconstruction method that ensures continuity of the interface and preserves volume fractions is presented here. It is made of two steps, first, the minimization of a cost functional based on volume fractions least square errors by using dynamic programming, a fast and efficient scheme well known in image processing, and then a local correction phase. In each cell, the interface is made of two line segments joining two edges. This new interface reconstruction method, called Dynamic Programming Interface Reconstruction has been coupled with various advection schemes, among them the Lagrange + remap scheme. With a reasonable computational cost, it has been observed in various test cases that Dynamic Programming Interface Reconstruction is more accurate and less diffusive compared with other existing classical reconstruction methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Incompressible multiphase flow and encapsulation simulations using the moment‐of‐fluid method

A moment‐of‐fluid method is presented for computing solutions to incompressible multiphase flows in which the number of materials can be greater than two. In this work, the multimaterial moment‐of‐fluid interface representation technique is applied to simulating surface tension effects at points where three materials meet. The advection terms are solved using a directionally split cell integrated semi‐Lagrangian algorithm, and the projection method is used to evaluate the pressure gradient force term. The underlying computational grid is a dynamic block‐structured adaptive grid. The new method is applied to multiphase problems illustrating contact‐line dynamics, triple junctions, and encapsulation in order to demonstrate its capabilities. Examples are given in two‐dimensional, three‐dimensional axisymmetric (R–Z), and three‐dimensional (X–Y–Z) coordinate systems. Copyright © 2015 John Wiley & Sons, Ltd.     

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.     

A discontinuous Galerkin‐based sharp‐interface method to simulate three‐dimensional compressible two‐phase flow

A numerical method for the simulation of compressible two‐phase flows is presented in this paper. The sharp‐interface approach consists of several components: a discontinuous Galerkin solver for compressible fluid flow, a level‐set tracking algorithm to follow the movement of the interface and a coupling of both by a ghost‐fluid approach with use of a local Riemann solver at the interface. There are several novel techniques used: the discontinuous Galerkin scheme allows locally a subcell resolution to enhance the interface resolution and an interior finite volume Total Variation Diminishing (TVD) approximation at the interface. The level‐set equation is solved by the same discontinuous Galerkin scheme. To obtain a very good approximation of the interface curvature, the accuracy of the level‐set field is improved and smoothed by an additional P_NP_M‐reconstruction. The capabilities of the method for the simulation of compressible two‐phase flow are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3. Copyright © 2015 John Wiley & Sons, Ltd.     

Interface reconstruction with least‐square fit and split Eulerian–Lagrangian advection

Two new volume‐of‐fluid (VOF) reconstruction algorithms, which are based on a least‐square fit technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF/PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagrangian and Eulerian split advection algorithms is investigated in detail and a new mixed split Eulerian implicit–Lagrangian explicit (EI–LE) scheme is presented. This method conserves the mass to machine error, performs better than split Eulerian and Lagrangian algorithms, and it is only slightly worse than unsplit schemes. However, the combination of the interface reconstruction with the least‐square fit and its advection with the EI–LE scheme appears superior to other existing approaches. Copyright © 2003 John Wiley & Sons, Ltd.     

Development of a compressive surface capturing formulation for modelling free‐surface flow by using the volume‐of‐fluid approach

With the aim of accurately modelling free‐surface flow of two immiscible fluids, this study presents the development of a new volume‐of‐fluid free‐surface capturing formulation. By building on existing volume‐of‐fluid approaches, the new formulation combines a blended higher resolution scheme with the addition of an artificial compressive term to the volume‐of‐fluid equation. This reduces the numerical smearing of the interface associated with explicit higher resolution schemes while limiting the contribution of the artificial compressive term to ensure the integrity of the interface shape is maintained. Furthermore, the computational efficiency of the the higher resolution scheme is improved through the reformulation of the normalised variable approach and the implementation of a new higher resolution blending function. The volume‐of‐fluid equation is discretised via an unstructured vertex‐centred finite volume method and solved via a Jacobian‐type dual time‐stepping approach. Copyright © 2012 John Wiley & Sons, Ltd.     

A simple sliding‐mesh interface procedure and its application to the CFD simulation of a tidal‐stream turbine

An effective way of using computational fluid dynamics (CFD) to simulate flow about a rotating device—for example, a wind or marine turbine—is to embed a rotating region of cells inside a larger, stationary domain, with a sliding interface between. This paper describes a simple but effective method for implementing this as an internal Dirichlet boundary condition, with interfacial values obtained by interpolation from halo nodes. The method is tested in two finite‐volume codes: one using block‐structured meshes and the other unstructured meshes. Validation is performed for flow around simple, isolated, rotating shapes (cylinder, sphere and cube), comparing, where possible, with experiment and the alternative CFD approach of fixed grid with moving walls. Flow variables are shown to vary smoothly across the sliding interface. Simulations of a tidal‐stream turbine, including both rotor and support, are then performed and compared with towing‐tank experiments. Comparison between CFD and experiment is made for thrust and power coefficients as a function of tip‐speed ratio (TSR) using Reynolds‐averaged Navier–Stokes turbulence models and large‐eddy simulation (LES). Performance of most models is good near the optimal TSR, but simulations underestimate mean thrust and power coefficients in off‐design conditions, with the standard k– ? turbulence model performing noticeably worse than shear stress transport k– ω and Reynolds‐stress‐transport closures. LES gave good predictions of mean load coefficients and vital information about wake structures but at substantial computational cost. Grid‐sensitivity studies suggest that Reynolds‐averaged Navier–Stokes models give acceptable predictions of mean power and thrust coefficients on a single device using a mesh of about 4 million cells. Copyright © 2013 John Wiley & Sons, Ltd.     

Validation of CFD‐CSD coupling interface methodology using commercial codes

Coupling interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is required to provide exchange of information for the simulation of fluid–structure interaction (FSI) phenomena. Accuracy and consistency of information exchanged through coupling interface between the independent CFD and CSD solvers plays a central role in the simulation and prediction of FSI phenomenon, like flutter. In this paper validation of an implemented coupling interface methodology is presented for subsonic, transonic and near supersonic mach regime. The test case chosen for this purpose is the flutter of AGARD445.6 standard I‐wing weakened model configuration for subsonic to near transonic flow regime. Gambit^® and Fluent^® are used for CFD grid generation and solution of fluid dynamic equations, respectively. CSD modeling and simulation are provided by numerical time integration of modal dynamic equations derived through the finite element modeling in ANSYS^® environment. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling of two‐dimensional laminar flow using finite element method

In this paper, a Galerkin weighted residual finite element numerical solution method, with velocity material time derivative discretisation, is applied to solve for a classical fluid mechanics system of partial differential equations modelling two‐dimensional stationary incompressible Newtonian fluid flow. Classical examples of driven cavity laminar flow and laminar flow past a cylinder are presented. Numerical results are compared with data found in the literature. Copyright © 1999 John Wiley & Sons, Ltd.     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.