Note on two formulations of Crank-Nicolson method for Navier-Stokes equations
Document Type
Article
Publication Date
12-12-2024
Department
Department of Mathematical Sciences
Abstract
We consider two formulations of the Crank-Nicolson (CN) method for the Navier-Stokes equations (NSE). The “natural” way of implementing CN for NSE is formally second order accurate in time for both velocity and pressure, whereas another formulation approximates pressure with only first order accuracy in time. Both versions of the method are applied to the benchmark problem of computing drag and lift in the flow around a cylinder. We show that the presumably more accurate version of the CN can create a solution with nonphysical oscillations and give incorrect predictions for the maximal drag coefficient, whereas the other formulation of the method predicts the drag and lift coefficients more accurately and does not introduce nonphysical oscillations. We locate the source of the issue and suggest several remedies.
Publication Title
Numerical Algorithms
Recommended Citation
Labovsky, A.,
&
Schwiebert, K.
(2024).
Note on two formulations of Crank-Nicolson method for Navier-Stokes equations.
Numerical Algorithms.
http://doi.org/10.1007/s11075-024-01983-w
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1301