Shahbaz, Khosro and Paraschivoiu, Marius and Mostaghimi, Javad
Second order accurate volume tracking based on remapping for triangular meshes.
Journal of Computational Physics, 188
Official URL: http://dx.doi.org/doi:10.1016/S0021-9991(03)00156-...
This paper presents a second order accurate piecewise linear volume tracking based on remapping for triangular meshes. This approach avoids the complexity of extending unsplit second order volume of fluid algorithms, advection methods, on triangular meshes. The method is based on Lagrangian–Eulerian (LE) methods; therefore, it does not deal with edge fluxes and corner fluxes, flux corrections, as is typical in advection algorithms. The method is constructed of three parts: a Lagrangian phase, a reconstruction phase and a remapping phase. In the Lagrangian phase, the original, Eulerian, grid is projected along trajectories to obtain Lagrangian grids. In practice, this projection is handled through the time integration of velocity field for grid vertices at each time step. The reconstruction is based on truncating the volume material polygon for each Lagrangian mixed grid. Since in piecewise linear approximation, the interface is represented by a segment line, the polygon material truncation is mainly finding the segment interface. Finding the segment interface is calculating the line normal and line constant at each multi-fluid cell. Details of applying two normal calculation methods, differential and geometric least squares (GLS) methods, are given. While the GLS method exhibits second order accurate approximation in reproducing circular interfaces, the differential least squares (DLS) method results in a first order accurate representation of the interface. The last part of the algorithm which is remapping of the volume materials from the Lagrangian grid to the original one is performed by a series of polygon intersection procedures. The behavior of the algorithm is investigated for flow fields with constant interface topology and flow fields inducing large interfacial stretching and tearing. Second order accuracy is obtained if the velocity integration as well as the reconstruction steps are at least second order accurate.
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