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Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains.
- Source :
- AIP Advances; Jun2014, Vol. 4 Issue 6, p1-29, 29p
- Publication Year :
- 2014
-
Abstract
- The finite difference method (FDM) based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21583226
- Volume :
- 4
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- AIP Advances
- Publication Type :
- Academic Journal
- Accession number :
- 97019136
- Full Text :
- https://doi.org/10.1063/1.4885555