CONVERGENCE ANALYSIS ON THE GIBOU-MIN METHOD FOR THE HODGE PROJECTION
- 주제(키워드) Hodge projection , finite volume method , Poisson equation , Gibou-Min
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 INT PRESS BOSTON, INC
- 발행년도 2017
- URI http://www.dcollection.net/handler/ewha/000000147317
- 본문언어 영어
초록/요약
The Hodge projection of a vector field is the divergence-free component of its Helmholtz decomposition. In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. In the decomposition by the Gibou-Min method, an important L-2-orthogonality holds between the gradient field and the solenoidal field, which is similar to the continuous Hodge decomposition. Using the orthogonality, we present a novel analysis which shows that the convergence order is 1.5 in the L-2-norm for approximating the divergence-free vector field. Numerical results are presented to validate our analyses.
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