Improving accuracy of volume penalised fluid-solid interactions

We analyse and improve the volume-penalty method, a simple versatile way to model objects in fluid flows. The method is kind of fictitious-domain that approximates no-slip boundary conditions with rapid linear damping inside object. can then simulate complex, moving general numerical solvers without specialised algorithms or boundary-conforming grids. Volume penalisation pays for this simplicity by introducing an equation-level error, $\textit{model error}$, related time $\eta \ll 1$. While error has been proven vanish as tends zero, previous work suggests convergence at slow rate $\mathcal{O}(\eta^{1/2})$. stiffness implies conventional volume only achieves first order accuracy. using multiple-scales matched-asymptotics signed-distance coordinate system valid arbitrary smooth geometries. show dominant stems from displacement length proportional Reynolds number $\text{Re}$ dependent layer size $\mathcal{O}(\eta^{1/2}\text{Re}^{-1/2})$. relative leads multiple regimes. Our key finding derives smoothing prescription eliminates reduces $\mathcal{O}(\eta)$ all This translates second validate our findings several comprehensive benchmark problems finally combine Richardson extrapolation correction further $\mathcal{O}(\eta^{2})$.