JOURNAL OF COMPUTATIONAL PHYSICS | 卷:335 |
Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains | |
Article | |
Stein, David B.1  Guy, Robert D.1  Thomases, Becca1  | |
[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA | |
关键词: Embedded boundary; Immersed boundary; Incompressible Navier Stokes; Fourier spectral method; Complex geometry; High-order; | |
DOI : 10.1016/j.jcp.2017.01.010 | |
来源: Elsevier | |
【 摘 要 】
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.
【 授权许可】
Free
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
10_1016_j_jcp_2017_01_010.pdf | 1453KB | download |