Volume Of Fluid Function Research Articles

A new algorithm to simulate the dynamics of a glacier: theory and applications

AbstractWe propose a novel Eulerian algorithm to compute the changes of a glacier geometry for given mass balances. The surface of a glacier is obtained by solving a transport equation for the volume of fluid (VOF). The surface mass balance is taken into account by adding an interfacial term in the transport equation. An unstructured mesh with standard stabilized finite elements is used to solve the non-linear Stokes problem. The VOF function is computed on a structured grid with a high resolution. The algorithm is stable for Courant numbers larger than unity and conserves mass to a high accuracy. To demonstrate the potential of the algorithm, we apply it to reconstructed Late-glacial states of a small valley glacier, Vadret Muragl, in the Swiss Alps.

Computational Modeling of Macroscopic Transportation in Continuous Castings

Macroscopic transportation in a continuous casting is modeled using the SIMPLER algorithm and the finite difference method. The simulation software Visual Cast has been developed to describe meniscus profile, fluid flow, solidification and centreline segregation based on the volume of fluid function and the mass, momentum, energy, and species conservation equations. It is found that the meniscus profile is coherently related to the position of circumfluence in the continuous casting mold. When the vortex above the flow jet from the nozzle is close to the meniscus, the level fluctuation becomes prominent. The centreline segregation is affected by the thermosolutal convection. The species concentration in the mush of the strand rises quickly and reaches a maximum at the end of the solidification.

A topology optimization approach using VOF method

Topology optimization methods with continuous design variables obtained by the homogenization formula or the solid isotropic microstructure with penalty (SIMP) model are widely used in the layout of structures. In the implementation of these approaches, one must take into account several issues, e.g., irregularity of the problem, occurrence of the checkerboard pattern, and intermediate density. To suppress these phenomena, the employment of additional strategies such as the perimeter control or the filtering method will be required. In this paper, a topology optimization method which can eliminate these difficulties is developed based on the volume of fluid (VOF) method. In the method, shape design is described in terms of the VOF function. Since this function is defined by a volume fraction of material occupying each element, it can be recognized as a continuous material density in the SIMP model. Within the framework of the VOF analysis, the topology optimization procedure is reduced to a convection motion of the material density governed by a Hamilton–Jacobi equation as in the level set method. Through numerical examples, the validity of the proposed method is investigated.

An immersed boundary method for incompressible flows using volume of body function

AbstractA simple and effective immersed boundary method using volume of body (VOB) function is implemented on unstructured Cartesian meshes. The flow solver is a second‐order accurate implicit pressure‐correction method for the incompressible Navier–Stokes equations. The domain inside the immersed body is viewed as being occupied by the same fluid as outside with a prescribed divergence‐free velocity field. Under this view a fluid–body interface is similar to a fluid–fluid interface encountered in the volume of fluid (VOF) method for the two‐fluid flow problems. The body can thus be identified by the VOB function similar to the VOF function. In fluid–body interface cells the velocity is obtained by a volume‐averaged mixture of body and fluid velocities. The pressure inside the immersed body satisfies the same pressure Poisson equation as outside. To enhance stability and convergence, multigrid methods are developed to solve the difference equations for both pressure and velocity. Various steady and unsteady flows with stationary and moving bodies are computed to validate and to demonstrate the capability of the current method. Copyright © 2005 John Wiley & Sons, Ltd.

Estimating curvature from volume fractions

An interface represented by discrete, abruptly-varying volume fractions poses particular challenges for the accurate estimation of interfacial curvature. Most approaches within a volume-of-fluid (VOF) framework do not estimate curvature directly from the VOF function, but instead from a smoothly-varying function derived from some mapping (e.g., convolution, discrete quadrature) of the VOF function. In this study we assess and compare the accuracy and robustness of curvature estimates derived from three smooth, VOF-based functions: a convolved VOF (CV) function, a height function (HF), and a reconstructed distance function (RDF). The methodology used in reconstructing a distance function from volume fractions is new and therefore presented in detail along with an analysis of the resulting sensitivities. We find that curvature estimates derived from the height function provide superior results, as measured in smaller error and higher (second-order) convergence rate. While curvature estimates from the RDF provides smaller errors relative to those derived from the CV, both techniques exhibit similar convergence behaviour. Numerical results, including a new cosine wave verification test, are presented to substantiate the findings.

An efficient method for capturing free boundaries in multi‐fluid simulations

AbstractAn easy‐to‐use front capturing method is devised by directly solving the transport equation for a volume of fluid (VOF) function. The key to this method is a semi‐Lagrangian conservative scheme, namely CIP_CSL3, recently proposed by the author. In the CIP_CSL3 scheme, the first‐order derivative of the interpolation polynomial at each cell centre is used to control the shape of the reconstructed profile. We show in the present paper that the first‐order derivative, which plays a crucial role in reconstructing the interpolation profile, can also be used to eliminate numerical diffusion. The resulting algorithm can be directly used to compute the VOF‐like function and retain the compact thickness of the moving interface in multi‐fluid simulations. No surface reconstruction based on the value of VOF function is required in the method, which makes it quite economical and easy to use. The presented method has been tested with various interfacial flows including pure rotation, vortex shearing, multi‐vortex deformation and the moving boundaries in real fluid as well. The method gives promising results to all computed problems. Copyright © 2003 John Wiley & Sons, Ltd.