RBC3D

Spectral boundary integral solver for cell-scale flows

Authors: S. H. Bryngelson, H. Zhao, A. Isfahani, J. B. Freund

RBC3D is a flow solver for soft capsules and cells via the methods discussed in Zhao et al., JCP (2010) and more. This codebase solves the boundary integral form of the Stokes equations via an algorithm tailored for cell-scale simulations:

• Spectrally-accurate spherical harmonics represent the deforming surfaces
• Modified Green’s function approximation used for near-range interactions
• Electrostatic-like repulsion prevents cells from intersecting
• Weak-formulation of no-slip boundary conditions (e.g., vessel walls)
• These features ensure that simulations are robust. Parallel communication via MPI enables large simulations, such as model vascular networks.

Installation

To install on a mac from the cloned repository, you can

shell brew install gcc mpich gfortran pkg-config wget cmake ./rbc.sh install-mac

and then from the RBC3D root directory, run these commands but replace .zshrc with where you store environment variables:

shell rootdir=`pwd` echo -e "export PETSC_DIR=$rootdir/packages/petsc-3.21.3 \nexport PETSC_ARCH=arch-darwin-c-opt" >> ~/.zshrc

Then to execute and run a case, you can: shell mkdir build cd build cmake .. make -j 8 minicase # or just `make` to make common and all the cases cd minicase mpiexec -n 1 ./minit mpiexec -n 2 ./mtube # number of nodes can be changed

This will generate output files in build/minicase/D. To keep output files in examples/minicase/D and use input files in examples/minicase/Input, you can do this instead once files are built in the build directory:

shell cd examples/case mpiexec -n 1 ../../build/case/minit mpiexec -n 2 ../../build/case/mtube

To run a case with more cells and nodes, you should use a supercomputing cluster. Instructions on how to build RBC3D on a cluster are available here.

Papers that use RBC3D

This is an attempt to document the papers that make use of RBC3D.

• Zhao, H., Isfahani, A. H., Olson, L. N., & Freund, J. B. (2010). A spectral boundary integral method for flowing blood cells. Journal of Computational Physics, 229(10), 3726-3744. https://doi.org/10.1016/j.jcp.2010.01.024
• Freund, J. B., & Orescanin, M. M. (2011). Cellular flow in a small blood vessel. Journal of Fluid Mechanics, 671, 466-490. https://doi.org/10.1017/S0022112010005835
• Isfahani, A. H., & Freund, J. B. (2012). Forces on a wall-bound leukocyte in a small vessel due to red cells in the blood stream. Biophysical journal, 103(7), 1604-1615. https://doi.org/10.1016/j.bpj.2012.08.049
• Freund, J. B., & Shapiro, B. (2012). Transport of particles by magnetic forces and cellular blood flow in a model microvessel. Physics of fluids, 24(5), 051904. https://doi.org/10.1063/1.4718752
• Freund, J. B. (2013). The flow of red blood cells through a narrow spleen-like slit. Physics of Fluids, 25(11), 110807. https://doi.org/10.1063/1.4819341
• Freund, J. B., & Vermot, J. (2014). The wall-stress footprint of blood cells flowing in microvessels. Biophysical Journal, 106(3), 752-762. https://doi.org/10.1016/j.bpj.2013.12.020
• Boselli, F., Freund, J. B., & Vermot, J. (2015). Blood flow mechanics in cardiovascular development. Cellular and Molecular Life Sciences, 72, 2545-2559. https://doi.org/10.1007/s00018-015-1885-3
• Bryngelson, S. H., & Freund, J. B. (2018). Global stability of flowing red blood cell trains. Physical Review Fluids, 3(7), 073101. http://doi.org/10.1103/PhysRevFluids.3.073101
• Bryngelson, S. H., & Freund, J. B. (2018). Floquet stability analysis of capsules in viscous shear flow. Joural of Fluid Mechanics, 852, 663–677. http://doi.org/10.1017/jfm.2018.574
• Bryngelson, S. H., & Freund, J. B. (2019). Non-modal Floquet stability of a capsule in large amplitude oscillatory extension. European Journal of Mechanics B/Fluids, 77, 171–176. http://doi.org/10.1016/j.euromechflu.2019.04.012
• Bryngelson, S. H., Guéniat, F., & Freund, J. B. (2019). Irregular dynamics of cellular blood flow in a model microvessel. Physical Review E, 100, 012203. http://doi.org/10.1103/PhysRevE.100.012203

License

MIT.