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
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
An immersed boundary method with direct forcing for the simulation of particulate flows
Journal of Computational Physics
An improved direct-forcing immersed-boundary method for finite difference applications
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Short Note: A moving-least-squares reconstruction for embedded-boundary formulations
Journal of Computational Physics
Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems
Journal of Computational Physics
A boundary condition capturing immersed interface method for 3D rigid objects in a flow
Journal of Computational Physics
Hi-index | 31.46 |
Direct forcing methods are a class of methods for solving the Navier-Stokes equations on nonrectangular domains. The physical domain is embedded into a larger, rectangular domain, and the equations of motion are solved on this extended domain. The boundary conditions are enforced by applying forces near the embedded boundaries. This raises the question of how the flow outside the physical domain influences the flow inside the physical domain. This question is particularly relevant when using a projection method for incompressible flow. In this paper, analysis and computational tests are presented that explore the performance of projection methods when used with direct forcing methods. Sufficient conditions for the success of projection methods on extended domains are derived, and it is shown how forcing methods meet these conditions. Bounds on the error due to projecting on the extended domain are derived, and it is shown that direct forcing methods are, in general, first-order accurate in the max-norm. Numerical tests of the projection alone confirm the analysis and show that this error is concentrated near the embedded boundaries, leading to higher-order accuracy in integral norms. Generically, forcing methods generate a solution that is not smooth across the embedded boundaries, and it is this lack of smoothness which limits the accuracy of the methods. Additional computational tests of the Navier-Stokes equations involving a direct forcing method and a projection method are presented, and the results are compared with the predictions of the analysis. These results confirm that the lack of smoothness in the solution produces a lower-order error. The rate of convergence attained in practice depends on the type of forcing method used.