In the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on Cartesian grids is presented. In the proposed method an arbitrary three-dimensional solid surface immersed in the fluid is discretized using an unstructured, triangular mesh, and all the Cartesian grid nodes near the interface are identified. Then, the solution at these nodes is reconstructed via linear interpolation along the local normal to the body, in a way that the desired boundary conditions for both pressure and velocity fields are enforced. The overall accuracy of the resulting solver is second-order, as it is demonstrated in two test cases involving laminar flow past a sphere.
Bibliographical noteFunding Information:
A.G. and F.S. were supported by NSF Career Grant 9875691, a grant from Oak Ridge National Laboratory and DOE, and NIH Grant RO1-HL-07262. E.B. was supported by NIH Grant RO1-HL-07262 and a grant from the Minta Martin Foundation.
- Cartesian grids
- Direct forcing
- Finite-difference method
- Immersed boundaries