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This thesis presents the results obtained from the implementation of a numerical method to simulate multiphase flows using dynamic unstructured meshes. The Navier-Stokes equations are obtained using the arbitrary Lagrangian-Eulerian (ALE) formulation, are discretized using the Galerkin finite element method. A projection method based on approximated block LU decomposition is employed to decouple acceleration and pressure. The interface between the imiscible fluids is represented by edges and vertices belonging to the triangulation, and the interface tension is computed using a distribution technique based on the gradient of a Heaviside function. The mesh is moved using a mesh velocity, computed from a combination between the fluid velocity and an elastic velocity. The elastic velocity is computed based on a Laplacian filter over the position of the mesh points. To control the quality of the elements in the triangulation, a dynamic mesh control procedure is employed, in which points are inserted and deleted based on Delaunay triangulations. Additionally, a smooth distribution of the edge sizes in the mesh is computed using the error estimated by the Hessian of the velocities. We present validations for one and two-fluid simulations, comparing the results to analytical expressions, experimental data and numerical results from other methods available in the literature with good agreement. Additionally, an application to the simulation of bubbly flows is carried out, and the comparisons to another numerical technique are presented.

Simulação de escoamentos multifásicos em malhas não estruturadas