期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 335, 期 -, 页码 155-178出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.01.010
关键词
Embedded boundary; Immersed boundary; Incompressible Navier Stokes; Fourier spectral method; Complex geometry; High-order
资金
- National Science Foundation [DMS-1160438.]
- Direct For Mathematical & Physical Scien [1160438] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1160438] Funding Source: National Science Foundation
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this work, we extend the IBSE method to allow for the imposition of a divergence constraint, and demonstrate high-order convergence for the Stokes and incompressible Navier Stokes equations: up to third-order pointwise convergence for the velocity field, and second-order pointwise convergence for all elements of the stress tensor. The method is flexible to the underlying discretization: we demonstrate solutions produced using both a Fourier spectral discretization and a standard second-order finite-difference discretization. (C) 2017 Elsevier Inc. All rights reserved.
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