A Chebyshev - Legendre spectral method for the transient solutions of flow past a solid sphere
- EG G Idaho, Inc., Idaho Falls (United States)
- Washington State Univ., Pullman (United States)
A full spectral model for the stream-function-vorticity formulation is developed for the solution of unsteady flow past a rigid sphere. To convert the governing partial differential equations to discrete form, Chebyshev and Legendre polynomials are employed to expand the vorticity and stream function in the radial and angular directions, respectively, together with a first-order, fully implicit, iterative scheme for time advancement. The solution to the system of discrete nonlinear equations is accomplished by LU decomposition in conjunction with the influence matrix to resolve the lack of vorticity boundary conditions. Owing to the global nature of the orthogonal trial functions, the present technique provides a means to achieve highly accurate results with less number of unknowns than either traditional finite difference or finite element methods. Comparisons of numerical solutions with previous results show consistent trends as reported in studies dealing with Cartesian coordinates.
- OSTI ID:
- 6605630
- Journal Information:
- Journal of Computational Physics; (United States), Vol. 104:2; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
FLUID FLOW
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTION
UNSTEADY FLOW
BOUNDARY CONDITIONS
CARTESIAN COORDINATES
FUNCTIONS
ITERATIVE METHODS
LEGENDRE POLYNOMIALS
MATRICES
CALCULATION METHODS
COORDINATES
DIFFERENTIAL EQUATIONS
EQUATIONS
POLYNOMIALS
420400* - Engineering- Heat Transfer & Fluid Flow