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Efficient and Highly Accurate Computation of a Class of Radially Symmetric Solutions of the Navier–Stokes Equation and the Heat Equation in Two Dimensions

✍ Scribed by Henrik O. Nordmark

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
191 KB
Volume
142
Category
Article
ISSN
0021-9991

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✦ Synopsis

In this paper we test several different formulas for the computation of the exact vorticity and angular velocity in certain radially symmetric solutions of the twodimensional Navier-Stokes equation in vorticity-stream function form. The class of initial conditions for the vorticity considered here has often been used by many authors in the study of vortex methods. However, only in the case of zero viscosity has it been possible to efficiently compute the exact vorticity and velocity at later times. The expressions for the vorticity and angular velocity, given in this paper, enable us to compute these quantities both efficiently and highly accurately for nonzero viscosity. This makes it feasible to obtain reliable error measurements in the study of vortex methods for the Navier-Stokes equation.

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