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Simulation of Taylor-Couette flow. I. Numerical methods and comparison with experiment. (English) Zbl 0561.76037
We present a numerical method that allows us to solve the Navier-Stokes equation with boundary conditions for the viscous flow between two concentrically rotating cylinders as an initial-value problem. We use a pseudospectral code in which all of the time-splitting errors are removed by using a set of Green functions (capacitance matrix) that allows us to satisfy the inviscid boundary conditions exactly. For this geometry we find that a small time-splitting error can produce large errors in the computed velocity field. We test the code by comparing our numerically determined growth rates and wave speeds with linear theory and by comparing our computed torques and wave speeds with experimentally measured values and with the values that appear in other published numerical simulations.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
76-04 Software, source code, etc. for problems pertaining to fluid mechanics
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