We present a second order ensemble method based on a blended three-step BDF timestepping scheme to compute an ensemble of Navier-Stokes equations. Compared with the only existing second order ensemble method that combines the two-step BDF timestepping scheme and a special explicit second order Adams-Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method.
We present a second-order ensemble method based on a blended three-step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier-Stokes equations. Compared with the only existing second-order ensemble method that combines the two-step BDF timestepping scheme and a special explicit second-order Adams-Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method.
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second order
second-order
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BDF
backward differentiation formula (BDF)
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second order
second-order
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second order
second-order