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We present an improved and modified formulation of the dual time–stepping technique which makes use of two derivatives in pseudo–time. This new technique, based on the critically damped harmonic oscillator, retains the convergence properties to the stationary solution. Furthermore, when compared with the conventional time–marching, the dual time– stepping with two derivatives reduces the stiffness of the problem and requires fewer iterations for full convergence to steady–state.

IMPROVED DUAL TIME–STEPPING USING SECOND DERIVATIVES