EPSRC Reference: 
GR/K58166/01 
Title: 
SETTLING OF SPHERICAL PARTICLES IN VISCOELASTIC FLUIDS USING A MOVING SPECTRAL ELEMENT METHOD 
Principal Investigator: 
Phillips, Professor TN 
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Department: 
Inst of Mathematical and Physical Sci 
Organisation: 
Aberystwyth University 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 January 1996 
Ends: 
31 December 1997 
Value (£): 
91,341

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Summary on Grant Application Form 
A moving spectral element method is developed for the numerical simulation of timedependent viscoelastic flow around a sphere falling along the axis of a cylinder. A fully coupled implicit algorithm is used for the temperal discretization. A spectral element mesh, part of which moves with the sphere, is used. Pseudospectral approximations are used for each dependent variable in each spectral element.A weak formulation of the equations generates a system of nonlinear algebraic equations which can be written as an implicit system for the stresses. Newton's method is used to solve this system. The Jacobian is approximated using finite difference and the stress update is determined using the GMRES algorithm. Efficient preconditioners are constructed for this iterative method. The algorithm is validated for an Oldroyd B fluid. Boger fluids are simulated using the ChilcottRallison model and comparisons are made with experiments. The dependence of the drag on the sphere on viscoelasticity and on the ratio of sphere to tube radius is studied.

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