LOCALIZED RADIAL BASIS FUNCTIONS AND DIFFERENTIAL QUADRATURE-MESHLESS METHOD FOR SIMULATING COMPRESSIBLE FLOWS

摘要

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.