Application On Premixed Turbulent V-Flame Simulation And Shape Recovery Problem By Level Set Method

This dissertation focuses on the discussion of application on the simulation of premixed turbulent V-flame and shape recovery problem by level set method. The main contents include the following aspects:Firstly, we introduce the main two mathematical models of front tracking problem:one is the boundary value function to compute the arrival time of the front as it crosses each point. The other one is the initial value function to embed the interface as the zero level set of a time-dependent level set functionφ, and obtain the position of interface by solving a level set equation. The main approach to solve this problem is the level set method we discuss in this paper.Then we introduce two traditional techniques for tracking interface. One is the marker particle method, which uses particles to marker the equal intervals divided from the interface. By recording the information of moving particles, the position of interface is tracked. The other one is the volume-of-fluid(VOF) method which uses a VOF function F to record the information of the flow in each cell, and evolves F to track the interface.Secondly, the algorithm and application of level set method are discussed carefully. We consider how to construct the level set functionφas a signed distance function such as the zero level set ofφdenotes the interface. And some numerical techniques such as upwind scheme, ENO, WENO and TVD RK method are introduced to solve the level set equation to obtain the instantaneous value ofφ.Meanwhile, in order to maintain 0 as a signed distance function during the computation progress, we consider a re-initialization scheme which is solved by fast marching method commonlyThirdly, the largest disadvantage of level set method is the lack of conserva-tion especially in the region with high curvature. To overcome it, we introduced three kinds of modified level set method:Coupled Level Set (CLS) method, conservative level set method and particle level set method.Fourthly, after discussing the main idea and recent work of level set method, we propose a new conservative level set method-velocity reconstructed level set method combined the bi-cubic interpolation with Newton's method to replace the velocity of the grid points with the velocity of interface. By this means, the conservation is guaranteed without using the re-initialization schemes. We test the efficiency of this method by comparing the results with the experimental results on the simple vortex problem and the simulation of premixed turbulent V-flame problem.Finally, we propose a new approach through an iteration algorithm based on level set method to solve the shape recovery problem by using the level set function to overcome the high ill-posed problem caused by the discontinuity of parameters.