Mr Stephen Wade

Office: 666 | Telephone: +61 8 8313 1605

Research seminars

Doctoral thesis

Mathematical modelling of free-surface flows

Honours thesis

Analysis and implementation of smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) is a particle method for solving complex geometry flows based on kernel estimation. The choice of kernel and the spatial derivative formulations used in SPH, and the evaluation of the resulting numerical consistency and stability of standard formulations is reviewed. The results of the analysis has strong implications for the inter- pretation of simulations when the particle distribution becomes irregular, as in these situations consistency is not possible with traditional formulations. In spite of a low order of accuracy, SPH is used widely in practise. The reasons for this are that it often conforms well with theoretical and experi- mental observations due in part to symmetry in the formulation which leads to physical conservation laws being treated to a high degree of accuracy. Couette flow is a simple theoretical flow of fluid between two infinitely flat parallel planes which are moving along their tangent space. A 2D analytic solution is used to compare to results of SPH simulation of a weakly com- pressible fluid initially at rest subject to the Couette flow boundaries. The results show that for relatively low Reynolds number ∼ 160 the simulation appears stable, but for higher Reynolds number ∼ 800 the particles become disordered and the solution diverges before an equillibrium is reached.