Speaker
Mr
Ludvig af Klinteberg
(KTH Numerical Analysis)
Description
We present a method for simulating periodic suspensions of sedimenting rigid
particles, based on a boundary integral solution of the Stokes flow equations. The
purpose of our work is to improve the understanding of the large scale properties of
suspensions by looking at the microscale interactions between individual particles.
Boundary integral methods are attractive for this problem type due to high attainable
accuracy, depending on the underlying quadrature method, and a reduction of the
problem dimensionality from three to two. However, the resulting discrete systems
have full matrices, and require the use of fast algorithms for efficient solution.
Our method is based on a periodic version of the completed double layer boundary
integral formulation for Stokes flow, which yields a well-conditioned system that
converges rapidly when solved iteratively using GMRES. The discrete system is
formulated using the Nyström method, and the singular integrals of the formulation
are treated using singularity subtraction.
The method is accelerated by a spectrally accurate fast Ewald summation method,
which allows us to compute the single and double layer potentials of the formulation
in O(N log N) time. By developing accurate estimates for the truncation errors of the
Ewald summation, we are able to choose the parameters of the fast method such
that the computation time is optimal for a given error tolerance.
Primary author
Mr
Ludvig af Klinteberg
(KTH Numerical Analysis)
Co-author
Prof.
Anna-Karin Tornberg
(KTH Numerical Analysis)
