GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
On the effect of numerical errors in large eddy simulations of turbulent flows
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Algorithm for direct numerical simulation of emulsion flow through a granular material
Journal of Computational Physics
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
3D vesicle dynamics simulations with a linearly triangulated surface
Journal of Computational Physics
Applying a second-kind boundary integral equation for surface tractions in Stokes flow
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
Hi-index | 31.47 |
A spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated. The blood cells are modeled as finite-deformation elastic membranes containing a higher viscosity fluid than the surrounding plasma, but the solver itself is independent of the particular constitutive model employed for the cell membranes. The surface integrals developed for solving the viscous flow, and thereby the motion of the massless membrane, are evaluated using an O(NlogN) particle-mesh Ewald (PME) approach. The cell shapes, which can become highly distorted under physiologic conditions, are discretized with spherical harmonics. The resolution of these global basis functions is, of course, excellent, but more importantly they facilitate an approximate de-aliasing procedure that stabilizes the simulations without adding any numerical dissipation or further restricting the permissible numerical time step. Complex geometry no-slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine. The implementation is verified against solutions for axisymmetric flows reported in the literature, and its accuracy is demonstrated by comparison against exact solutions for relaxing surface deformations. It is also used to simulate flow of blood cells at 30% volume fraction in tubes between 4.9 and 16.9@mm in diameter. For these, it is shown to reproduce the well-known non-monotonic dependence of the effective viscosity on the tube diameter.