Interpolation error in DNS simulations of turbulence: consequences for particle tracking

An important aspect in numerical simulations of particle laden turbulent flows is the interpolation of the flow field. For the interpolation different approaches are used. Where some studies use low order linear interpolation others use high order spline methods. We compare several interpolation methods and conclude that interpolation based on B-spline functions has several advantages compared with traditional methods. First, B-spline interpolation can be executed very efficiently by optimal use of the pseudo spectral code, only one FFT needs to be executed where Hermite spline needs multiple FFTs for computing the derivatives. Second, the smoothness of the interpolated field is higher than that of Hermite spline interpolation. Finally, the interpolation error almost matches the one of Hermite spline which is not reached by the other methods investigated. Further, we focus on estimating the interpolation error and compare it with the discretisation error of the flow field. In this way one can balance the errors in order to achieve an optimal result. Algorithms have been developed for the approximation of the interpolation error. As a spin-off of the theoretical analysis a practical method is proposed which enables direct estimation of the interpolation error from the energy spectrum, which may provide a quantitative indicator for this purpose.