A new volume of fluid method in three dimensions-Part II: Piecewise-planar interface reconstruction with cubic-Bézier fit (original) (raw)
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Journal of Computational Physics, 2007
We present and analyse two new Volume-of-Fluid (VOF) reconstruction algorithms that approximate the interface separating two immiscible fluids as a linear function in each grid cell (PLIC -Piecewise Linear Interface Calculation). The first one is based on two simple geometrical criteria for the reconstruction of a linear interface, the second one minimizes a distance functional to find the plane coefficients. Their performance is tested for several smooth surfaces. The geometrical nature of operator split advection is quicklyreviewed and a new three-dimensional split advection algorithm is presented. It is exactly mass conserving for a divergence-free velocity field and its accuracy rapidly increases as the CFL number is decreased. Secondorder convergence is found in the case of velocity fields with not uniform vorticity at high grid resolutions in the asymptotic regime.
A numerical method for interface reconstruction of triple points within a volume tracking algorithm
Mathematical and Computer Modelling, 2008
A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a triple point is described as the minimum of a constrained minimization problem inside an interfacial cell of the discretization. For given volume fractions of materials in the cell, an interior-point/Newton method is used for the reconstruction of the local geometry and the localization of the triple point. Initialization of the Newton method is performed with a derivative-free algorithm. Numerical results are presented for static and pure advection cases to illustrate the efficiency and robustness of the algorithm.
Journal of Computational Physics, 2006
We present an adaptive coupled level-set/volume-of-fluid (ACLSVOF) method for interfacial flow simulations on unstructured triangular grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a discontinuous Galerkin finite element method. The volume fraction advection is performed using a Lagrangian-Eulerian method. The interface is reconstructed based on both the level set and the volume fraction information. In particular, the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction. Different from previous works, we have developed an analytic method for finding the line constant on triangular grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. The level set function is finally reinitialized to the signed distance to the reconstructed interface. Since the level set function is continuous, the normal vector calculation is easy and accurate compared to a classic volume-of-fluid method, while tracking the volume fraction is essential for enforcing mass conservation. The method is also coupled to a finite element based Stokes flow solver. The code validation shows that our method is second order and mass is conserved very accurately. In addition, owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately.
JCP, 2003
In the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on Cartesian grids is presented. In the proposed method an arbitrary three-dimensional solid surface immersed in the fluid is discretized using an unstructured, triangular mesh, and all the Cartesian grid nodes near the interface are identified. Then, the solution at these nodes is reconstructed via linear interpolation along the local normal to the body, in a way that the desired boundary conditions for both pressure and velocity fields are enforced. The overall accuracy of the resulting solver is second-order, as it is demonstrated in two test cases involving laminar flow past a sphere.
Journal of Mechanical Science and Technology, 2009
Direct numerical simulation of multiphase flow on fixed Eulerian grid became increasingly popular due to its simplicity and robustness. Some of the well-known methods include VOF, Level Set, Phase field, and Front Tracking method. Lately, hybridization of above methods gets its attention to overcome the disadvantages pertaining to each method. One hybrid approach developed by the author is the Level Contour Reconstruction Method (LCRM) which combines characteristics of both Front Tracking and Level Set method. Many engineering problems also contain complex geometry as boundary condition and proper representation of grid structure plays very important role for the successful outcomes. In this paper, an algorithm for handling arbitrary geometry inside fixed Eulerian computational domain with multiphase flow has been presented. Interface reconstruction between liquid and vapor phase has been performed outside of arbitrary solid boundary explicitly along with dynamic contact angle model. Sharp interface technique using ghost fluid point extrapolation method has been utilized for correct implementation of no-slip boundary condition at the wall.
Accurate representation of surface tension using the level contour reconstruction method
Journal of Computational Physics, 2005
Some of the most demanding tests of interface methods for two-phase flows with surface tension which use fixed Eulerian grids occur at the two extremes of highly dynamic flows or static equilibrium conditions. It has been difficult to design an interface method to operate accurately across this spectrum especially for 3D fluid flow calculations which, on the one hand, do not often have the required grid resolution to capture all of the fine scale structures that typically appear in highly stretched interfaces nor, on the other hand, the required accuracy in calculating surface tension forces. We present improvements to the interface reconstruction procedure in the level contour reconstruction method (LCRM) [J. Comput. Phys. 180 , which now allow the reconstruction to proceed using a locally instead of a globally calculated contour value. These improvements allow more precise control of the interface reconstruction in highly dynamic flows with coalescence and rupture and also avoid the problem of local mass redistribution in poorly resolved calculations. In addition, a new hybrid technique for surface tension calculation in the context of the front tracking method is demonstrated and shown to result in a marked improvement in suppressing parasitic currents by generally two orders of magnitude. We compare and validate these new procedures in various test cases.
Aiaa Journal, 2010
Finite volume discretizations on unstructured grids that are more than second-order-accurate have not yet gained wide acceptance. This is due to the high computational cost and memory requirements of the proposed schemes and the technical difficulties in achieving a high-order-accurate solution. It is especially true when considering flows in complex geometries. In this paper, a third-order cell-centered finite volume discretization is detailed that is based on quadratic data recovery, which is computationally efficient and has optimal memory requirements. The densitybased flow-solver discretization and solution algorithm are described briefly, followed by a detailed presentation of the least-squares-based multistep quadratic data-reconstruction methodology proposed here. The paper is concluded with numerical examples to verify the accuracy and numerical efficiency of this high-order finite volume discretization.
Journal of Computational Physics, 2007
Multiphase flows associated with interfacial dynamics, steep jumps in fluid properties and moving boundaries between different phases pose substantial computational challenges in terms of both modeling as well as computational efficiency. The present work extends a marker-based immersed boundary, or front tracking, technique to model the three-dimensional interfacial dynamics. It tracks the moving boundary using triangulated surface grids and solves the flow governing equations on a stationary Cartesian grid. A locally adaptive grid is employed to help meet the resolution requirements based on the interface location and solution features. The interface resolution is controlled via a conservative restructuring technique satisfying mass continuity. An improved level contour reconstruction algorithm for topology change, preserving the interface connectivity information, is presented highlighting various algorithmic difficulties and implemented remedies. The outlines of a finite-volume, staggered grid Navier-Stokes solution using the projection method are discussed. The impact of conservative interface restructuring and reconstruction has been assessed against mass-conservation and spurious velocity errors. The overall capabilities of the developed algorithms have been demonstrated for large density ratios, O(1000), interfacial flows using various rising bubbles and drop collision/coalescence computations involving coalescence and break-up dynamics.