engleski

Automatic Mesh Motion in FVM

There exists a number of physical phenomena in which the continuum solution couples with additional equations which influence the shape of the domain or the position of an internal interface. Examples of such cases include multi-phase flows, where the interface between the phases is captured by the mesh, solid-fluid interaction, where the motion and deformation of a solid changes the shape of the fluid domain etc. In this work we shall present a general-purpose moving mesh Finite Volume (FV) methodology developed to simulate such cases. The main difficulty in tackling cases with variable geometry is maintaining of the mesh quality. Out of several possible approaches to the problem, we have chosen the deforming mesh method. Here, the computational mesh is adjusted to the shape of the boundary which is updated in every step of the transient simulation. It therefore remains to determine the motion of all points internal to the mesh based on the prescribed motion of its boundary. Several deforming mesh approaches have been presented in the past, mainly based on the spring analogy. However, this approach proved to lack robustness, particularly for arbitrarily unstructured meshes common in FV simulations. Having reviewed the requirements on the mesh motion solver in terms of mesh regularity we have settled on a vertex based FE-type solver which operates on arbitrary polyhedra. A new type of second-order polyhedral “ motion element” consistent with the FV mesh handling has been developed. In the FE mesh motion framework described above, we can choose several candidate equations to govern the mesh motion. The most obvious choices are the Laplace equation with constant and variable diffusivity and the small-strain formulation of the linear elastic model. The three choices have been investigated on a number of simple test cases and the variable diffusivity Laplace equation has been selected as optimal, together with the set of rules for specifying the diffusivity field. The methodology is validated on several test cases in 2- and 3-D in order to examine its limitations in terms of Co number and robustness. Finally, the automatic moving mesh FV algorithm is applied to a two-phase simulation of a free-rising air bubble in water. Here, the fluid equations are solved in both phases and coupled across the free surface. The free surface is represented as a mesh interface whose motion depends on the local pressure differences and surface tension.

Numerical Modelling; Finite Volume Method; Automatic Mesh Motion

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