Continuity constrained least-squares interpolation for SFO suppression in immersed boundary methods

A new immersed boundary interpolation for discrete forcing methods is presented. The method decreases spurious oscillations in the pressure field and consequently in the body force calculations which are a common issue in several immersed boundary methods. The method applies a continuity constraint in the least-squares interpolation, and guarantees that adjacent interpolation polynomials are continuous between each other. This approach strictly enforces continuity in the flow reconstruction domain, reducing time discontinuities caused by the boundary conditions applied at the immersed boundary. Several moving body problems test cases are simulated, including a three dimensional one, to demonstrate the new method's capability of computing stable pressure fields, even for coarse grids and small CFL numbers, which are known to increase the pressure oscillations.