Some techniques for improving the resolution of finite difference component-wise WENO schemes for polydisperse sedimentation models

Polydisperse sedimentation models can be described by a system of conservation laws for the concentration of each species of solids. Some of these models, as the Masliyah–Locket–Bassoon model, can be proven to be hyperbolic, but its full characteristic structure cannot be computed in closed form. Component-wise finite difference WENO schemes may be used in these cases, but these schemes suffer from an excessive diffusion and may present spurious oscillations near shocks. In this work we propose to use a flux-splitting that prescribes less numerical viscosity for component-wise finite difference WENO schemes. We compare this technique with others to alleviate the diffusion and oscillatory behavior of the solutions obtained with component-wise finite difference WENO methods.