A fast algorithm for particle simulations
Journal of Computational Physics
Applied Mathematics and Computation
Boundary conditions for viscous vortex methods
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical simulation of hydrodynamics by the method of point vortices
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
The blob projection method for immersed boundary problems
Journal of Computational Physics
Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry
Journal of Computational Physics
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
Journal of Computational Physics
Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods
Journal of Computational Physics
An immersed boundary method with direct forcing for the simulation of particulate flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
A Cartesian grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
Numerical simulation of the fluid dynamics of 2D rigid body motion with the vortex particle method
Journal of Computational Physics
Analysis of Direct Three-Dimensional Parabolic Panel Methods
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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This article presents numerical analysis and practical considerations for three-dimensional flow computation using an implicit immersed boundary method. The Euler equations, or half a step of the Navier-Stokes equations when using fractional step algorithms, are investigated in their vorticity formulation. The context of flow computation around an arbitrarily shaped body is especially investigated. In conventional immersed boundary methods using vorticity, singular vortex are dispatched over the body surface. In the present study, one prefers using sources of potential velocity field, dispatched on the body, whose nature is not vorticity. Such a formulation is compatible to the Euler equations. In practice, these sources of potential flow produce a velocity through this surface, aiming in practice at cancelling a flow-through velocity. This article focuses on the use of the source-to-flow-through linear application, its properties being the key points for fast convergence. Its self-adjointness, or lack thereof, conditioning and preconditioning aspects are investigated. It follows that computing a velocity field with no-flow-through conditions in complex geometry, when using the source-to-flow-through linear application, can be achieved for 4/3 of the computational cost of standard Poisson equation in a Cartesian box. The robustness of immersed boundaries is especially interesting when used together with vortex-in-cell methods, well known for their robustness in time and their ability to compute accurately convective effects. A few examples, based on real-world geometries, illustrate the method capabilities.