Adaptive moment-of-fluid method

Abstract

A novel adaptive mesh refinement (AMR) strategy based on the moment-of-fluid (MOF) method for volume-tracking of evolving interfaces is presented. Moment-offluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids. The mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process. The centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments. A new Lagrange+remap scheme is presented for advecting moments, which includes Lagrangian backtracking, polygon intersectionbased remapping and forward tracking to define the material centroid. The effectiveness and efficiency of AMR-MOF method is demonstrated with classical test problems, such as Zalesak's disk and reversible vortex problem. The comparison with previously published results for these problems shows the superior accuracy of the AMR-MOF method over other methods. In addition, two new test cases with severe deformation rates are introduced, namely droplet deformation and S-shape deformation problems, for further demonstration of the capabilities of the AMR-MOF method. Fig. 1. Conceptual structure of the adaptive mesh refinement strategy for interfacial flow computation. In volume-tracking methods (MOF or VOF), the Interface Representation module is typically composed of (i) interface reconstruction and (ii) advection steps.

Compressible, multiphase semi-implicit method with moment of fluid interface representation

“…The interface is chosen as the piece-wise linear reconstruction, Γ m i (3.3), that exactly captures the volume fraction and minimizes error in the centroid. Centroid error can be interpreted as curvature in the interface, which can be used as a condition for mesh refinement in AMR algorithms [3].…”

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

“…Then the diffusion equations in (3) are solved in both Ω − and Ω + with the new interface location given by the zero-contour of φ at time t n+1 . Dirichlet boundary conditions are imposed on the interface using the Gibbs-Thomson relation in equation (4). When computing the Gibbs-Thomson relation, we use the value of the normal velocity V · n at time t n , but the interface curvature κ is computed at time t n+1 to reflect the updated morphology of the front.…”

“…Therefore, the velocity field must be extended to the nodes in a small band on each side of the interface by constant extrapolation in the normal direction. The rationale for extrapolations in the normal direction is based on the fact that the interface propagates only in its normal direction 4 . The extrapolation procedures we use are those of [8], detailed in section 4.2.…”

“…In additions, adaptive framework have been introduced (see e.g. [138,15,3,14,143,76,51,19,137,10,92,4,111,41,25,58,128,66] and the references therein).…”

“…In the Stefan problem, surface tension is modeled through the − c κ term in the GibbsTompson boundary condition (4). Figure 24 depicts the growth history of a square solid seed.…”