Gaussian-Like Immersed Boundary Kernels with Three Continuous Derivatives and Improved Translational Invariance
arXiv:1505.07529 · doi:10.1016/j.jcp.2016.04.024
Abstract
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 new 5-point and 6-point immersed-boundary kernels that are and yield a substantially improved translational invariance compared to other common IB kernels.
arXiv comment10 pages, 4 figures. This is an updated manuscript to the published version with a new 5-point kernel
References in corpus (2)
Cited by in corpus (25)
- Rapid Sampling of Stochastic Displacements in Brownian Dynamics Simulations
- Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
- Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods
- Gaussian-Like Immersed Boundary Kernels with Three Continuous Derivatives and Improved Translational Invariance
- An Immersed Boundary Method with Divergence-Free Velocity Interpolation and Force Spreading
- A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions
- Drag, lift and torque correlations for axi-symmetric non-spherical particles in locally non-uniform flows
- A Design-Based Model of the Aortic Valve for Fluid-Structure Interaction
- An immersed interface-lattice Boltzmann method for fluid-structure interaction
- Coarse-graining the dynamics of immersed and driven fiber assemblies
- On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method
- A hybrid immersed boundary method for dense particle-laden flows
- A one-sided direct forcing immersed boundary method using moving least squares
- Brownian Dynamics of Fully Confined Suspensions of Rigid Particles Without Green's Functions
- Microstructure-based prediction of hydrodynamic forces in stationary particle assemblies
- Computing hydrodynamic interactions in confined doubly-periodic geometries in linear time
- A Discrete Ion Stochastic Continuum Overdamped Solvent Algorithm for Modeling Electrolytes
- Controlled Comparison of Simulated Hemodynamics across Tricuspid and Bicuspid Aortic Valves
- Modeling Electrokinetic Flows with the Discrete Ion Stochastic Continuum Overdamped Solvent Algorithm
- Regularized Stokes Immersed Boundary Problems in Two Dimensions: Well-posedness, Singular Limit, and Error Estimates
- Steric effects in induced-charge electro-osmosis for strong electric fields
- Image-based immersed boundary model of the aortic root
- 2D force constraints in the method of regularized Stokeslets
- New Immersed Boundary Method with Irrotational Discrete Delta Vector for Droplet Simulations with Large Density ratio
- On immersed boundary kernel functions: a constrained quadratic minimization perspective