Localized Radial Basis Functions and Differential Quadrature-Meshless Method for Simulating Compressible Flows
Document Type
Article
Publication Date
1-1-2019
Publication Title
Computational Thermal Sciences: An International Journal
Volume
11
Issue
5
First page number:
401
Last page number:
422
Abstract
A numerical approach based on the meshless method is used to simulate compressible flow. The meshless, or mesh-free, method circumvents the need to generate a mesh. Since there is no connectivity among the nodes, the method can be easily implemented for any geometry. However, one of the most fundamental issues in numerically simulating compressible flow is the lack of conservation, which can be a source of unpredictable errors in the solution process. This problem is particularly evident in the presence of steep gradient regions and shocks that frequently occur in highspeed compressible flow problems. To resolve this issue, a conservative localized meshless method based on radial basis functions and differential quadrature (RBF-DQ) has been developed. An upwinding scheme, based on the Roe method, is added to capture steep gradients and shocks. In addition, a blended RBF is used to decrease the dissipation ensuing from the use of low shape parameters. A set of test problems are used to confirm the accuracy and reliability of the algorithm, and the method applied to the solution of Euler's equation.
Keywords
Meshless method; Compressible flow; Radial basis function
Disciplines
Mechanical Engineering
Language
English
Repository Citation
Nabizadeh, E.,
Pepper, D. W.
(2019).
Localized Radial Basis Functions and Differential Quadrature-Meshless Method for Simulating Compressible Flows.
Computational Thermal Sciences: An International Journal, 11(5),
401-422.
http://dx.doi.org/10.1615/ComputThermalScien.2019025846