Numerical simulation of combustion using mesh-free methods

该研究涉及二维平面或轴对称圆柱流动问题的湍流燃烧计算建模。研究将集中在以下几个方面：1。使用水平集建模来定义湍流的燃烧和未燃烧界面。在这些界面所包围的连续区域中，将结合水平集方法使用无网格径向基函数。采用无网格径向基函数法对内部连续区域的解进行时间推进。我们将使用Goetingen大学的Robert Schaback教授开发的Greedy算法。该算法被证明是非常有效的，因为它只使用那些重要的数据中心，在有限单元方法所需的计算时间的一小部分内减少残余误差。此外，还将实现移动数据中心方案，以进一步减少空间和时间截断误差。这一方案将限制在每一次前进时保持质量、动量分量和总能量。我们打算分两部分公布我们的结果：A.数值算法的详细描述，B.描述不同几何形状、障碍物放置等的数值结果，重点是计算效率。预计研究结果将为社会带来好处，包括提高用于预测实际燃烧器性能和排放特性的燃烧模拟的准确性和效率。该项目是由化学和运输系统部和数学科学部共同资助的，是美国国家科学基金会数学科学优先领域的一部分。

Public Abstract (CTS-0500505) The research involves computational modeling of turbulent combustion for two-dimensional planar or axisymmetric cylindrical-flow problems. The study will focus upon the following aspects:1. The use of level-set modeling to define the burnt and unburnt interfaces of turbulent flow.2. In the continuous regions bounded by such interfaces, mesh-free radial basis functions will be used in conjunction with the level-set methodology.The mesh-free radial basis function method will be used to time advance the solution in the interior continuous regions. We shall use the Greedy algorithm developed by Prof. Robert Schaback at Goetingen University. This algorithm is shown to be very efficient since it only uses those data centers important to reduce the residual errors at a fraction of the computational time required by finite element methods. In addition, a moving-data-center scheme will be implemented to further reduce both spatial and temporal truncation errors. This scheme will be constrained to conserve mass, momentum components and total energy at each time advance. We intend to publish our results in two parts: A. A detailed description of the numerical algorithm, and B. Numerical results describing different geometries, placement of obstacles, etc. with emphasis on computational efficiency. It is expected that the results of the research will provide benefits to society, including improved accuracy and efficiency of combustion simulations that are used to predict performance and emissions characteristics of practical combustors. This project is jointly funded by the Chemical and Transport Systems Division and the Division of Mathematical Sciences as part of the NSF Mathematical Sciences Priority Area.