Direct numerical simulation of three-dimensional isotropic turbulence with smoothed particle hydrodynamics

This study presents an investigation of the capability of smoothed particle hydrodynamics (SPH) to simulate three-dimensional isotropic turbulence. The effect of the error introduced by the particle disorder is assessed by comparing the standard Lagrangian SPH with an Eulerian adaptation. For the free decay of isotropic turbulence in a triple periodic box, the Eulerian SPH shows very good agreement with the reference solution, while the particle disorder in Lagrangian simulations yields an incorrect prediction of turbulent energy spectra. For the first time, a SPH investigation on linearly forced isotropic turbulence is also conducted with a focus on how the numerical dissipation affects the obtained solution. It is found that by using a Godunov-type SPH scheme for the continuity equation and by employing Roe's approximate solver for the Riemann problem at the interface of each neighboring particle, a stable solution is obtained, which is also in agreement with the results predicted by the theory of homogeneous isotropic turbulence. The efficacy of the particle shifting technique applied to turbulent SPH flows is studied in the end. Numerical findings indicate that corrective terms derived from the arbitrary Lagrangian-Eulerian theory are essential for a proper estimation of turbulence characteristics.