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Title: Sharp interface schemes for multi-material computational fluid dynamics
Author: Cutforth, Murray Connelly
ISNI:       0000 0004 7972 9637
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2019
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In this thesis we consider the solution of compressible multi-material flow problems, where each material is governed by the Euler equations and the material interface may be considered to be a perfect discontinuity separating macroscopic pure-material regions. Working in the framework of Godunov-type finite volume methods, we develop numerical algorithms for tracking the material interface and evolving fluid states. For the task of tracking the location of sharp material interfaces, we focus on volume tracking methods due to their ability to conserve mass in highly deformational flows. Three original contributions are presented in this area. First, the accuracy of the volume-of-fluid algorithm is improved through the addition of marker particles. Next, the efficient moment-of-fluid method is presented. This improves the computational efficiency of the moment-of-fluid method by a factor of three by mapping certain quantities during the interface reconstruction step on to a pre-computed data structure. Finally, a general framework for updating volume fractions based on the solution to a quadratic programming problem is presented. The evolution of fluid states in the full multi-material system is an independent problem. We present developments to two numerical approaches for this problem. The first, the ghost fluid method, is widely used due to the ease in which pure-fluid algorithms can be extended to the multi-material case. We investigate the effect of using a number of different interface tracking methods on the solutions, and find that the conservation errors vary by more than an order of magnitude. The ghost fluid method is then altered such that the ghost state extrapolation step is eliminated from the algorithm, allowing volume fraction-based interface tracking methods to be coupled. In the final chapter, we tackle the same problem using a mixture model-based method. The numerical method presented here is based on work by Miller and Puckett in 1996, in which a six-equation system using the assumption of pressure and velocity equilibrium was used to model two-material flow. We have thoroughly overhauled this method, incorporating Riemann solvers developed for the five-equation system, as well as a robust implicit energy update. We present numerical results on a range of one- and two-dimensional shock-interface interaction test problems which demonstrate the ability of the method to match the solutions from the five-equation model while maintaining a perfectly sharp material interface.
Supervisor: Nikiforakis, Nikos ; Barton, Phillip Sponsor: AWE
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: Multi-material flow ; Euler equations ; Volume-of-fluid ; Moment-of-fluid