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Title: An efficient implicit mesh-free method to solve two-dimensional compressible euler equations
Authors: Chen, H.Q.
Shu, C. 
Keywords: Euler equations
Implicit method
Least-square approach
Lu-sgs algorithm
Rbf-dq method
Transonic compressible flows
Issue Date: Mar-2005
Citation: Chen, H.Q., Shu, C. (2005-03). An efficient implicit mesh-free method to solve two-dimensional compressible euler equations. International Journal of Modern Physics C 16 (3) : 439-454. ScholarBank@NUS Repository.
Abstract: Local radial basis function-based differential quadrature (RBF-DQ) method is a natural mesh-free approach, in which any derivative of a function at a point is approximated by a weighted linear sum of functional values at its surrounding scattered points. In this paper, the weighting coefficients in the spatial derivative approximation of the Euler equation are determined by using a weighted least-square procedure in the frame of RBFs, which enhances the flexibility of distributing points in the computational domain. An upwind method is further introduced to cope with discontinuities by using Roe's approximate Riemann solver for estimation of the inviscid flux on the virtual mid-point between the reference knot and its surrounding knot. The lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm, which is implemented in a matrix-free form like the one used in the finite-volume method, is introduced in the work to speed up the convergence. The proposed approach is validated by its application to simulate transonic flows over a NACA 0012 airfoil. It was found that the present mesh-free results agree very well with available data in the literature, and the implicit LU-SGS algorithm can greatly save the computational time as compared with explicit time marching methods. © World Scientific Publishing Company.
Source Title: International Journal of Modern Physics C
ISSN: 01291831
DOI: 10.1142/S0129183105007327
Appears in Collections:Staff Publications

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