Modification of the IDW method for numerical simulation of aerodynamics problems on large grids

Abstract

The work is dedicated to the issues of numerical modeling of the flow problems around moving bodies. A numerical method based on the finite volume method was chosen as the basic approach for calculation. The basic equations of the Navier-Stokes system of equations describing the flow of a viscous compressible gas and discretization schemes are given. The movement of boundaries, as a rule, leads to a change in control volumes, so there is a need to use methods for changing the computational mesh. The article discusses in detail the IDW method for deformation of computational mesh. The computational complexity of the basic method is estimated as O(n_in_b) (n_i  и n_b are the number of internal vertices and boundary vertices), which causes difficulties for industrially oriented problems. A key element in accelerating the procedure for changing the computational mesh is the use of the fast multipole method. Hierarchical data structures with graph theory methods applied to the chosen approach made it possible to reduce the complexity of the algorithm to O(n_ilog(n_b)) and ensure high-quality deformation of the computational mesh. Additionally, a method of distributing the computational load is proposed, which increased the algorithm working speed up to 80% on the characteristic problems of the aviation industry.