A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Stability characteristics of the virtual boundary method in three-dimensional applications
Journal of Computational Physics
The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems
Journal of Computational Physics
An immersed boundary method with direct forcing for the simulation of particulate flows
Journal of Computational Physics
Journal of Computational Physics
An improved direct-forcing immersed-boundary method for finite difference applications
Journal of Computational Physics
The immersed boundary method: A projection approach
Journal of Computational Physics
Journal of Computational Physics
Short Note: A moving-least-squares reconstruction for embedded-boundary formulations
Journal of Computational Physics
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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We present an immersed-boundary algorithm for incompressible flows with complex boundaries, suitable for Cartesian or curvilinear grid system. The key stages of any immersed-boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary (a line in 2D, a surface in 3D), and the spreading of a force field from the immersed boundary to the neighboring mesh points, to enforce the desired boundary conditions on the immersed-boundary points. We propose a technique that uses the Reproducing Kernel Particle Method [W.K. Liu, S. Jun, Y.F. Zhang, Reproducing kernel particle methods, Int. J. Numer. Methods Fluids 20(8) (1995) 1081-1106] for the interpolation and spreading. Unlike other methods presented in the literature, the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved, independent of the grid topology (uniform or non-uniform, Cartesian or curvilinear). The technique is easy to implement, and is able to maintain the order of the original underlying spatial discretization. Applications to two- and three-dimensional flows in Cartesian and non-Cartesian grid system, with uniform and non-uniform meshes are presented.