Stability DuFort-Frankel

A variety of explicit (Dufort-Frankel, Lax-Wendroff, Runge-Kutta) and implicit (approximate factorization, LU-SGS) or hybrid schemes have been employed for integration in time. Because of the complexity of the incompressible Navier-Stokes equations, stability analyses to determine critical time steps are difficult. As a general rule, the allowable time step for an explicit method is proportional to the ratio of the smallest grid size to the largest convective velocity (or the wave propagation speed for an artificial compressibility method). 

DuFort EC, Frankel SP (1953) Stability conditions in the numerical treatment of parabolic differential equations. 

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