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Boundary spectral methods for non‐lifting potential flows
Author(s) -
Hwang W. S.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980330)41:6<1077::aid-nme325>3.0.co;2-x
Subject(s) - mathematics , discretization , basis function , spectral method , boundary element method , quadrature (astronomy) , gaussian quadrature , laplace transform , algebraic equation , numerical integration , mathematical analysis , collocation (remote sensing) , basis (linear algebra) , spectral element method , integral equation , nyström method , finite element method , geometry , computer science , mixed finite element method , physics , nonlinear system , quantum mechanics , machine learning , electrical engineering , thermodynamics , engineering
The boundary spectral method for solving three‐dimensional non‐lifting potential problems is developed. This method combines spectral approximations and the direct numerical integration such as Gaussian quadrature or trapezoidal rules successfully. The singularities of the integral equation are completely removed by subtracting known solutions from the Laplace equation. After discretization, every element of the resultant matrix only contains integrals with non‐singular kernels. Therefore, all the integrals can be implemented easily and efficiently. By spectral approximations, the unknown variable is expressed as a truncated series of basis functions, which are orthogonal usually. Instead of solving the variables at collocation points in the conventional methods, the coefficients of basis functions are determined in the spectral approach. It is shown that the new method reduces a lot of number of unknowns, storage of matrix elements, and computer time for solving the algebraic equations. © 1998 John Wiley & Sons, Ltd.