# My Sandbox

This ‘README’ provides on overview of the content of my sandbox.

## Blood Flow Modeling

#### Code

• myembed.h: modified embed.h
• extension to 3D of interpolation and force computation on embedded boundaries;
• 2D/3D torque computation on embedded boundaries;
• Neumann boundary condition on embedded boundary (reverse engineering of the Dirichlet boundary condition);
• in update_tracer, u \cdot \nabla u now takes into account non-zero face-velocity uf boundary conditions on embedded boundaries;
• robust small cell treatment (see Colella et al., 2006, Schneiders et al., 2013).
• mypoisson.h: modified poisson.h
• in project, the r.h.s. \nabla \cdot u_f now takes into account non-zero face-velocity uf boundary conditions on embedded boundaries.
• mycentered: modified centered.h
• treatment of emmerged (solid to fluid, necessary to avoid spurious variations in drag and lift forces) and submerged (fluid to solid, necessary to avoid adaptation in solid embedded boundaries) cells;
• dedicated events for moving embedded boundaries and tracers on embedded boundaries.

#### Test cases for static embedded boundaries

• Stokes flow past a static sphere: test hydrodynamic force computation
• Rotational stokes flow around a static sphere: test hydrodynamic torque computation
• Moving sphere near a wall in a Stokes flow: test projection algorithm with non-zero Dirichlet boundary conditions

#### Test cases for moving embedded boundaries with passive scalar

• Translating cylinder at Re=40 and Pe=100:
• single projection and passive scalar on the bottom half ot the domain and Dirichlet boundary conditions f=0: moving_scalar1x.c
• double projection and passive scalar with Dirichlet boundary conditions f=1: moving_scalar1y.c
• Translating cylinder at Re=400: test Strouhal number St of the Bénard–von Kármán Vortex Street
• single projection and passive scalar with Pe=100 and Neumann boundary conditions \nabla f \cdot n = 1: moving_scalar2x.c
• double projection and passive scalar with Pe = 1 and Neumann boundary conditions \nabla f \cdot n = 1: moving_scalar2y.c

## References

 [schneiders2013] L. Schneiders, D. Hartmann, M. Meinke, and W. Schroder. An accurate moving boundary formulation in cut-cell methods. Journal of Computational Physics, 235:786–809, 2013. [colella2006] Phillip Colella, Daniel Graves, Benjamin Keen, and Modiano David. A cartesian grid embedded boundary method for hyperbolic conservation laws. Journal of Computational Physics, 211(1):347–366, 2006. [ http ] [guilmineau2002] E. Guilmineau and P. Queutey. A numerical simulation of vortex shedding from an oscillating circular cylinder. Journal of Fluids and Structures, 16:773–794, 2002. [dutsch1998] H. Dutsch, F. Durst, S. Becker, and H. Lienhart. Low-reynolds-number flow around an oscillating circular cylinder at low keulegan-carpenter numbers. Journal of Fluid Mechanics, 360:249–271, 1998. [okajima1982] A. Okajima. Strouhal numbers of rectangular cylinders. Journal of Fluid Mechanics, 123:379–398, 1982. [faxen1946] O.H. Faxen. Forces exerted on a rigid cylinder in a viscous fluid between two parallel fixed planes. Proc. R. Swed. Acad. Eng. Sci., 187:1–13, 1946.