Simple and accurate scheme for fluid velocity interpolation for Eulerian–Lagrangian computation of dispersed flows in 3D curvilinear grids

Particle tracking in turbulent flows in complex domains requires accurate interpolation of the fluid velocity field. If grids are non-orthogonal and curvilinear, the most accurate available interpolation methods fail. We propose an accurate interpolation scheme based on Taylor series expansion of the local fluid velocity about the grid point nearest to the desired location. The scheme is best suited for curvilinear grids with non-orthogonal computational cells. We present the scheme with second-order accuracy, yet the order of accuracy of the method can be adapted to that of the Navier–Stokes solver.An application to particle dispersion in a turbulent wavy channel is presented, for which the scheme is tested against standard linear interpolation. Results show that significant discrepancies can arise in the particle displacement produced by the two schemes, particularly in the near-wall region which is often discretized with highly-distorted computational cells.