Pointwise interactions of finite element modeling of advection-diffusion equations
Pointwise iteration techniques including successive under-relaxation (SUR), Gauss-Seidel (G-S), and successive over-relaxation (SOR) schemes, are applied to advection-diffusion equations to derive the matrix equation with finite element methods. These schemes are tested using two simple examples for which analytical solutions are available so that numerical results can be checked to ensure code consistency. Numerical experiments indicate that the iteration schemes, if convergent, produce almost identical solutions as those obtained by the direct elimination scheme. For diffusion dominant transport, all three iteration schemes generate convergent computations. However, for advection-diffusion equally dominant or advection dominant transport, only SUR and G-S schemes yield convergent calculations, the SOR scheme leads to divergent computations. Pointwise iteration schemes offer substantial savings in central process unit (CPU) memory over the direct elimination scheme, even for the small, two-dimensional verification example, without complicating the programming efforts and, in the meantime, keeps the CPU time comparable. A realistic, hypothetical problem is used to demonstrate the applicability and versatility of pointwise iterations and direct elimination schemes. The saving in CPU memory using the pointwise iterations is more than tenfold that using the direct elimination solution for this hypothetical problem. The saving in CPU time is even better, more than 40 fold.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 6652374
- Report Number(s):
- CONF-840762-2; ON: DE84015284
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ADVECTION
COMPUTER CALCULATIONS
DIFFUSION
FINITE ELEMENT METHOD
ITERATIVE METHODS
MASS TRANSFER
MATRICES
NUMERICAL SOLUTION
TRANSPORT THEORY