复杂无粘流场数值模拟的矩形/三角形混合网格技术

建立了一套模拟复杂无粘流场的矩形／三角形混合网格技术，其中三角形仅限于物面附近，发挥非结构网格的几何灵活性，以少量的网格模拟复杂外型；同时在以外的区域采用矩形结构网格，发挥矩形网格计算简单快速的优势，有效地克服全非结构网格计算方法需要较大内存量和较长ＣＰＵ时间的不足．混合网格系统由修正的四分树方法生成．将ＮＮＤ有限差分与ＮＮＤ有限体积格式有机地融合于混合网格计算，消除了全矩形网格模拟曲边界的台阶效应，同时保证了网格间的通量守恒．数值实验表明本方法在模拟复杂无粘流场方面的灵活性和高效性．

A CARTESIAN/TRIANGULAR HYBRID GRID SOLVER FOR COMPLEX INVISCID FLOW FIELDS

A Cartesian/triangular hybrid grid technique is presented for simulating complex inviscid flowfields, where the triangles are limited only close to the solid wall to describe arbitrary complicated curve boundaries,while the Cartesian grids cover almost entire area of interest. A hybrid solver is developed by coupling the non-oscillatory, non-free-parameter dissipative (NND) finite difference scheme and the NND finite volume scheme naturally to match Cartesian/triangular hybrid grids. The present method inherits the geometric flexibility of unstructured grids, and the computational simplicity and rapidness of the Cartesian tessellation, whereas avoids the staircasing effect of Cartesian cells on describing curve boundaries and releases the requirement of irregular meshes on more memory storage and CPU time. A data-shared treatment is introduced in interface regions to ensure the flux conservative condition between the two grid parts. The hybrid grid system is generated by a modified Quadtree method with a Cartesian background grid technique controlling the grid spatial distribution. The part of triangular grids is optimized by a smoother based on the `spring analogy' and a`diagonal exchange' process based on Delaunay criteria. Numerical experiments include transonic flows over the NACA0012 airfoil and unsteady flows of a moving shock wave in a bend tube with two circles.The computational results demonstrate the accuracy, efficiency and robustness of present method.