New Theory of Hybrid-Upwind Technique and Discrete Del Operator for Finite-Element Method

Tanahashi, Takahiko; Oki, Yoshiatsu

doi:10.1080/10618569608940749

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…In Equation (8), vector {c} is composed of unknown nodal values, while vector {s} results from the source term and natural boundary condition (2b). To evaluate these integrals, the discrete Del (Nabla) operator method proposed by Tanahashi and Oki [11] was used to save main memory and computational time.…”

Section: Spatial Discretizationmentioning

confidence: 99%

On streamline diffusion arising in Galerkin FEM with predictor/multi‐corrector time integration

Eguchi

2002

Numerical Methods in Fluids

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SUMMARYIn the present paper, the author shows that the predictor=multi-corrector (PMC) time integration for the advection-di usion equations induces numerical di usivity acting only in the streamline direction, even though the equations are spatially discretized by the conventional Galerkin ÿnite element method (GFEM). The transient 2-D and 3-D advection problems are solved with the PMC scheme using both the GFEM and the streamline upwind=Petrov Galerkin (SUPG) as the spatial discretization methods for comparison. The solutions of the SUPG-PMC turned out to be overly di usive due to the additional PMC streamline di usion, while the solutions of the GFEM-PMC were comparatively accurate without signiÿcant damping and phase error. A similar tendency was seen also in the quasi-steady solutions to the incompressible viscous ow problems: 2-D driven cavity ow and natural convection in a square cavity.

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Section: Spatial Discretizationmentioning

confidence: 99%