Figure 15

Execution times in seconds of \(r=0.062\) (left) and \(r=0.6526\) (right) case for single-threaded runs versus the number of nodes in the domain N. Open symbols denote meshless Navier–Stokes timings and filled symbols denote MLBM timings. The stopping criterion was the same as in the remaining tests. In both methods, the execution time is inversely proportional to the timestep length \(\delta t\). In both methods the diffusive scaling of the timestep length was used (\(\delta t \propto h(\varvec{x})^2\) in MNS and \(\delta t \propto \delta x^2 \propto h(\varvec{x})^2\) in MLBM) and as \(\delta x \propto N^{1/3}\) one obtains that the execution time should scale as \(N^{1.5}\). The dashed lines denote the 1.5-order slope. The execution times for \(r=0.062\) were extrapolated based on the physical time at which the simulation reached the stopping criterion and the execution time for a fixed number of iterations.