A Tree-based Unstructured Cylindrical Grid Generation Method And Its Applications To Solve Euler Equations

The grid-based numerical method has always been an important means in computational fluid dynamics,and its capability to discrete the computational domain and describe complex geometry is closely related to the grid generation method used.In order to accurately reflect specific geometries like bodies of revolution,a tree-based unstructured cylindrical grid generation method is developed in this paper based on the unstructured Cartesian method.First,according to the geometric features of bodies of revolution,the boundary of the farfield of the computational domain is determined based on the coordinate plane of the cylindrical coordinate system,and the physical computational domain is then formed together with the surface of the body.The tree-based unstructured cylindrical grid is generated by recursively subdivision based on the coordinate plane of the cylindrical coordinate system following the methods used in the tree-based unstructured Cartesian method.The tree-based data structure of the grid is constructed to conduct the rapid search of the grid information.The recursive adaptive refinement of the grid near the surface of the body is used to accommodate accurately with the geometry of bodies of revolution.The tree-based unstructured cylindrical grid generation method is established according to the methods mentioned above in this paper.According to the proposed grid generation method,a corresponding grid generation program is then developed using Fortran language.In this paper,cases of grid generation such as two-dimensional cylinder and cylinder with fin-like components mounted in radial directions are given.Combined with the local compression method,the case of grid generation with radial narrow gaps between fin-like components and bodies of revolution is given.The cases demonstrated that the proposed grid generation method is particularly suitable for the description of fin-like components mounted in radial directions and this capability also enables to cope easily with geometrically critical features like radial narrow gaps between fin-like deflectors and slender bodies of revolution.On this basis,the proposed grid generation method is extended to three-dimensional problems,and cases of grid generation such as three-dimensional Basic Finner Reference Projectile are given in this paper.Finally,based on the tree-based unstructured grid in the cylindrical coordinate system generated above,combined with Jameson's finite volume method,a flow solver was developed to solve Euler equations.The results of the flow simulations of several typical cases like two-dimensional cylinder and three-dimensional Basic Finner Reference Projectile are included to demonstrate the capability of the proposed grid generation.