气相爆轰高阶中心差分-WENO组合格式自适应网格方法研究

【作者】 刘国昭；

【导师】 张树道；

【作者基本信息】 中国工程物理研究院 ， 流体力学， 2007， 硕士

【摘要】 本文针对气相爆轰问题,主要研究采用高阶中心差分-WENO组合格式和自适应网格方法,数值模拟二维和三维气相爆轰波的结构.高阶中心差分-WENO组合格式有效地将高阶中心差分格式和加权基本无振荡格式(WENO)组合起来,在间断区域使用WENO格式计算通量,在光滑区域使用中心差分格式计算通量,重点研究组合方法.在组合方法上通过数值试验比较了多种选择,并分析了不同数值实验结果产生的原因.本文最后选择了优化后的一组组合参数,并结合一种基于流场结构特征的自适应网格技术用于数值计算.通过计算一维,二维激波问题,研究了这种方法的精度和效率.数值试验表明,这种方法精度高,分辨率高,计算量小.本文将高阶中心差分-WENO组合格式和自适应网格方法应用于气相爆轰数值计算.数值模拟二维和三维气相爆轰波非定常结构.数值模拟结果表明,本文发展的这种方法计算结果正确,清晰地反映了爆轰波面复杂的波系结构,以及周期性振荡过程,获得了较为满意的效果,计算结果表明本文的方法具有高精度,高分辨率和高效率的特点,在气相爆轰数值模拟中具有良好的应用前景.更多还原

【Abstract】 In this thesis, a high order hybrid Central-WENO AMR method is presented for the numerical simulation of two- and three-dimensinal gaseous detonation structures.The hybrid Central-WENO finite difference scheme composes the two schemes effectively where high gradients regions are computed with WENO scheme in order to capture the discontinuities while smooth regions are computed with more efficient and accurate central finite difference scheme. The thesis focuses on the composition mode, and chooses optimal transition function and parameters through numerical test cases. The adaptive mesh refinement grid is based on flow field structure.In order to test the performance of the method, including accuracy, resolution and efficiency, one- and two-dimensional shock-dynamic examples are calculated. The results have proved that the hybrid scheme with AMR method has good property of high-order, high-resolution, and high-efficiency.The hybrid method has been used in the numerical simulation of two- and three-dimensinal unsteady gaseous detonation. The numerical results have shown correctly and clearly the complex wave structures and dynamic physical processes. The method has good prospects for application in gaseous detonation.更多还原