TY - JOUR

T1 - A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance

AU - Bao, Yuanxun

AU - Kaye, Jason

AU - Peskin, Charles S.

N1 - Funding Information:
We thank Aleksandar Donev for many enlightening discussions on this work, and in particular for his suggestion to use the nonzero second moment condition as a postulate of the new 6-point IB kernel. Y. Bao was supported in part by the Air Force Office of Scientific Research under grant number FA9550-12-1-0356 , as well as the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC0008271 . J. Kaye was supported in part by the National Science Foundation under grants NSF DMS-1115341 and DMS-1016554 .
Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid described by Eulerian variables is coupled with the immersed structure described by Lagrangian variables via the use of the Dirac delta function. From a numerical standpoint, the Lagrangian force spreading and the Eulerian velocity interpolation are carried out by a regularized, compactly supported discrete delta function, which is assumed to be a tensor product of a single-variable immersed-boundary kernel. IB kernels are derived from a set of postulates designed to achieve approximate grid translational invariance, interpolation accuracy and computational efficiency. In this note, we present a new 6-point immersed-boundary kernel that is C3 and yields a substantially improved translational invariance compared to other common IB kernels.

AB - The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid described by Eulerian variables is coupled with the immersed structure described by Lagrangian variables via the use of the Dirac delta function. From a numerical standpoint, the Lagrangian force spreading and the Eulerian velocity interpolation are carried out by a regularized, compactly supported discrete delta function, which is assumed to be a tensor product of a single-variable immersed-boundary kernel. IB kernels are derived from a set of postulates designed to achieve approximate grid translational invariance, interpolation accuracy and computational efficiency. In this note, we present a new 6-point immersed-boundary kernel that is C3 and yields a substantially improved translational invariance compared to other common IB kernels.

KW - Discrete delta function

KW - Fluid-structure interaction

KW - Immersed boundary method

KW - Immersed-boundary kernel

KW - Translational invariance

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U2 - 10.1016/j.jcp.2016.04.024

DO - 10.1016/j.jcp.2016.04.024

M3 - Article

AN - SCOPUS:84963753268

VL - 316

SP - 139

EP - 144

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -