Research On Grid Optimization For Computational Fluid Dynamics

This paper aims at exploring the grid generation and grid optimization technologies for computational fluid dynamics, and it includes 6 chapters.In Chapter 1, the background and importance for this research firstly are introduced, then the development for grid generation and grid optimization technologies is surveyed, the summary for other chapters is talked about at the end of this chapter.In Chapter 2, a structured grid generation method for domains with complicated boundary is discussed. Based on the Winslow method of variational form and integrated it with grid untangling and area averaging technologies, a discrete functional is designed. By using the optimization algorithm to solve the minimization problem of the discrete functional, optimized grids can be generated. Numerical experiments show that this method is robust, and can be used to generate grids with good geometric qualities on complicated domain. This method inherits the advantages of the Winslow method, and overcomes some faults of the Winslow method.In Chapter 3, an iterative method for solving highly nonlinear grid generation equations is presented. For a class of highly nonlinear conservative equations derived from variational grid generation methods, the standard Picard iterative method cannot solve it correctly. This chapter presents a new Picard iterative solution method. Numerical results show that new numerical algorithm can solve these equations very well. In the reference [2], developing good numerical algorithms for solving these equations was regarded as an important open problem.In Chapter 4, an advancing reference Jacobian optimization-based grid rezone method is presented. Combining RJM with advancing-front method, this chapter presents a new strategy named advancing reference Jacobian method (ARJM). New method will advance the optimization process step by step from one part of the boundary of the computational region to the remaining part. At each step, taking two neighboring rows (or columns) as the boundaries of sub-region and the rear row (column) nodes using optimized nodes, the middle row (column) of Lagrangian nodes will be optimized by RJM. The analyses and numerical experiments show that ARJM is much faster than RJM, and the geometric qualities of rezoned grids given by ARJM are almost the same as or even better than those given by RJM, and the rezoned grids obtained by using ARJM are closer to the Lagrangian grids than those by using RJM. In Chapter 5, A new variational grid optimization method is presented. The functional used in this method comprises of two parts. One part is the common grid generation functional, such as the Winslow funcional, the other is the functional which measures the distance from the Lagrangian nodes to new nodes. The Lagrangian nodes are optimized by solving the Euler-Lagrange equations of the combined functional. Numerical experiments and the application show that the new grids optimized by this method not only have good geometric properties, but also keep the sense of Lagrangian grids. This method is effective for improving the accuracy of overall computation.In Chapter 6, the conclusion for this paper is presented, and the plan for future work is proposed.