Simulation of the fountain flow effect by means of the radial functions method (RFM)
Ramirez C., Daniel
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The purpose of this work is to simulate the fountain flow effect using a meshless technique (RFM) and, therefore, to explore the possibilities that the method offers for free surface problems. To the knowledge of the author, the fountain ow effect has not been simulated in the past by means of meshless techniques. In this thesis, a steady state was assumed for all simulations. This assumption is common in the literature and can be found for instance in [28, 27]. It originates from the consideration of a reference system that moves with the average velocity of the flow. For the flow in a slit, a power law model model with n varying between 0:6 and 1:1 was used to describe the variation of the viscosity with the shear rate. Another case considered in this thesis is the fountain flow of a Newtonian uid in an axisymmetric tube including the force of gravity. The organization of the thesis is as follows: Chapter 2 presents a brief overview of the literature corresponding to the simulation of the fountain flow effect. In Chapter 3, the Radial Functions Method is presented using the solution of the Poisson equation as an example. Chapter 4 deals with the implementation of the method to simulate the fountain flow effect; this entails the representation of the motion and continuity equations, and the appropriate boundary conditions (including the free boundary) in terms of Radial Basis Functions. The thesis ends with chapters corresponding to the conclusions derived from the simulations and a presentation of possible lines of research for future work.