Dirichlet boundary pressure conditions enabled by unfolded surface integration for adjoint-based 3D data assimilation

This study demonstrates a novel procedure that utilizes the planar implementation of the Omnidirectional Integration /Green Function Integral (ODI /GFI) method on unfolded outer surfaces of a 3D domain to provide Dirichlet boundary pressure conditions for adjoint-based data assimilation of 3D turbulent flows. Assuming the pressure gradient field is continuous and the instantaneous spatial distribution of error is random and homogeneous, this new procedure (Unfolded Surface Integration, USI) is able to reduce the computational cost by two orders of magnitude, while preserving sufficient accuracy of the reconstructed pressure values on the boundary surfaces without invoking excessive computation involvement through the 3D domain. To further reduce the computational cost, a Poisson solver with FFT coupled with the Dirichlet boundary pressure values is employed to accelerate the computation. Consistent with the 2D version of the work (Abassi et al., 2025), it is shown that the Dirichlet boundary condition enabled by this USI procedure of ODI/ GFI can significantly improve the accuracy of the numerical prediction of pressure, vorticity and velocity in 3D when dealing with error-embedded experimental data. This method is further applied to a tomographic PIV measurement of a turbulent cavity shear layer flow.