Remeshed Smoothed Particle Hydrodynamics for the Simulation of Viscous and Heat Conducting Flows

We present an extension of the classical scheme of smoothed particle hydrodynamics (SPH) for the accurate handling of diffusion terms in the momentum and energy equation of viscous and heat conducting flows. A key aspect of the present SPH approach is the periodic reinitialization (remeshing) of the particle locations, which are being distorted by the flow map. High-order moment conserving kernels are being implemented for this remeshing procedure leading to accurate simulations. The accuracy of the proposed SPH methodology is tested for a number of benchmark problems involving flow and energy transport. The results demonstrate that the proposed SPH methodology is capable of DNS quality simulations while maintaining its robustness and adaptivity.