A finite difference method for the slow motion of a sphere in a rotating fluid

  • S. C. R. Dennis
  • D. B. Ingham
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 141)


A numerical method for treating certain classes of problems in the theory of rotating fluids is given. The uniform, slow motion of a sphere in a viscous fluid has been examined in the case where the undisturbed fluid rotates with constant angular velocity ωo and the axis of rotation is taken to coincide with the line of motion. The Navier-Stokes equations can be written in the form of three coupled, nonlinear, elliptic partial differential equations. These equations are expressed in finite-difference form using a specialized technique which is everywhere second order accurate. It is based on an expansion of a finite-difference scheme which already exists in the literature and which involves the exponential function. By expanding the exponentials in powers of their exponents an approximation is arrived at which is particularly suitable for use in obtaining numerical solutions.

Some preliminary tests of the method have been carried out. The numerical results confirm the theoretical work of Childress (1963, 1964) when both the Reynolds number and Taylor number are small. The effects of varying the mesh size, position of the outer boundary and relaxation parameters have been investigated.


Relaxation Parameter Elliptic Partial Differential Equation Constant Angular Velocity Taylor Number Diagonal Dominance 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • S. C. R. Dennis
    • 1
  • D. B. Ingham
    • 2
  1. 1.Department of Applied MathematicsUniversity of Western OntarioLondonCanada
  2. 2.School of MathematicsUniversity of LeedsLeedsEngland

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