Evaluating the Stability of Numerical Schemes for Fluid Solvers in Game Technology

Figure 1

Solution of (1) obtained from the FDTD algorithm (FDTD1) (31). Plots display spatial structure, , for time steps (initial conditions), , , , and exhibiting the evolution of the nonlinear wave and the advective instability. The nonlinear wave has a propagation speed proportional to its amplitude; therefore, the crest of the perturbed wave structure moves faster than its base. As a result, the crest of the wave tries to overtake the smaller amplitudes requiring a multivalued solution, forbidden in this numerical framework resulting in instability. The FDTD solution plotted here exhibits the qualitative behaviour of the numerical methods used in this paper.