An Efficient Dynamic Mesh Generation Method for Complex Multi-Block Structured Grid

Aiming at a complex multi-block structured grid, an efficient dynamic mesh generation method is presented in this paper, which is based on radial basis functions (RBFs) and transfinite interpolation (TFI). When the object is moving, the multi-block structured grid would be changed. The fast mesh deformation is critical for numerical simulation. In this work, the dynamic mesh deformation is completed in two steps. At first, we select all block vertexes with known deformation as center points, and apply RBFs interpolation to get the grid deformation on block edges. Then, an arc-length-based TFI is employed to efficiently calculate the grid deformation on block faces and inside each block. The present approach can be well applied to both two-dimensional (2D) and three-dimensional (3D) problems. Numerical results show that the dynamic meshes for all test cases can be generated in an accurate and efficient manner.

[1]  Christian B. Allen,et al.  Efficient mesh motion using radial basis functions with data reduction algorithms , 2008, J. Comput. Phys..

[2]  C. Allen,et al.  Unified fluid–structure interpolation and mesh motion using radial basis functions , 2008 .

[3]  Martin D. Buhmann,et al.  Radial Basis Functions , 2021, Encyclopedia of Mathematical Geosciences.

[4]  Miguel R. Visbal,et al.  Accuracy and Coupling Issues of Aeroelastic Navier-Stokes Solutions on Deforming Meshes , 1997 .

[5]  Zongmin Wu,et al.  Compactly supported positive definite radial functions , 1995 .

[6]  Sp Fiddes,et al.  A 2D Navier-Stokes method for unsteady compressible flow calculations on moving meshes , 1998 .

[7]  H. Tsai,et al.  Unsteady Flow Calculations with a Parallel Multiblock Moving Mesh Algorithm , 2001 .

[8]  A. C. Faul,et al.  Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions , 1999, Adv. Comput. Math..

[9]  O. Amoignon,et al.  Mesh Deformation using Radial Basis Functions for Gradient-based Aerodynamic Shape Optimization , 2007 .

[10]  H. Wendland,et al.  Multivariate interpolation for fluid-structure-interaction problems using radial basis functions , 2001 .

[12]  Christian B Allen,et al.  CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation , 2008 .

[13]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[14]  Ken Badcock,et al.  A grid deformation technique for unsteady flow computations , 2000 .

[15]  Richard K. Beatson,et al.  Smooth surface reconstruction from noisy range data , 2003, GRAPHITE '03.

[16]  Holger Wendland,et al.  On the smoothness of positive definite and radial functions , 1999 .

[17]  H. Bijl,et al.  Mesh deformation based on radial basis function interpolation , 2007 .

[18]  A. Jameson,et al.  Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation , 1996 .

[19]  K. Bathe.  Finite Element Procedures , 1995 .

[20]  Carlos E. S. Cesnik,et al.  EVALUATION OF SOME DATA TRANSFER ALGORITHMS FOR NONCONTIGUOUS MESHES , 2000 .

[21]  W. J. Gordon,et al.  Transfinite mappings and their application to grid generation , 1982 .

[22]  F. M. Bos,et al.  Numerical simulations of flapping foil and wing aerodynamics: Mesh deformation using radial basis functions , 2010 .

[23]  Hester Bijl,et al.  Higher-order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations , 2007, J. Comput. Phys..

[24]  Guru P. Guruswamy,et al.  A parallel, multi-block, moving grid method for aeroelastic applications on full aircraft , 1998 .

[25]  Samareh Jamshid,et al.  A Grid Generation System for Multi-disciplinary Design Optimization , 2003 .