A Simulator for Droplet (Unfinished)

Now, I changed to my topic so I'm not developing this code now. I failed to make this solver, however I decided to make it open because some part of this code is working and it is worth to read for someone new to level set or weno method. If you found a reason of bug in this code, please report to issue tracker.

• Windows only.
• Visual Studio 2013
• Compiler : Intel C++ Compiler 14.0
• CPU : i7-2600 (I turned on AVX for optimization)

• Open asd2_vs2013/asd2_vs2013.sln
• Just build and run, recommend Release build mode

• 2D : Seems to be working
• 3D : not sure

• 2D : Seems to be working
• 2D Axisymmetric : It's running but it's not right answer
• 3D : Failed to run

• Sussman's work (1999)
• Subcell Fix

• 2D case : second-order differencing
• 2D Axisymmetric : Use factorization technique
• 3D : Use poisson equation to solve viscous term

• Conjugate Gradient Method : Use Intel MKL BLAS
• BiConjugate Gradient Stabilized Method : Use Intel MKL BLAS

• Viscous term : use Heaviside function to make implicit solver
• Pressure term : use Ghost Fluid Method

• Hu, Changqing, and Chi-Wang Shu. "Weighted essentially non-oscillatory schemes on triangular meshes." Journal of Computational Physics 150.1 (1999): 97-127.

• Sussman's Method : Sussman, Mark, Peter Smereka, and Stanley Osher. "A level set approach for computing solutions to incompressible two-phase flow." Journal of Computational physics 114.1 (1994): 146-159.
• Subell Fix (1) : Min, Chohong, and Frédéric Gibou. "A second order accurate level set method on non-graded adaptive cartesian grids." Journal of Computational Physics 225.1 (2007): 300-321.
• Subell Fix (2) : Min, Chohong. "On reinitializing level set functions." Journal of computational physics 229.8 (2010): 2764-2772.

• 2D Axisymmetric : Kang, Myungjoo, Hyeseon Shim, and Stanley Osher. "Level set based simulations of two-phase oil–water flows in pipes." Journal of Scientific Computing 31.1-2 (2007): 153-184.
• 3D : Lee, Byungjoon, and Myungjoo Kang. "Full 3D Simulations of Two-Phase Core–Annular Flow in Horizontal Pipe Using Level Set Method." Journal of Scientific Computing (2015): 1-27.

• Kang, Myungjoo, Ronald P. Fedkiw, and Xu-Dong Liu. "A boundary condition capturing method for multiphase incompressible flow." Journal of Scientific Computing 15.3 (2000): 323-360.
• Liu, Xu-Dong, Ronald P. Fedkiw, and Myungjoo Kang. "A boundary condition capturing method for Poisson's equation on irregular domains." Journal of computational Physics 160.1 (2000): 151-178.
• Hong, Jeong-Mo, and Chang-Hun Kim. "Discontinuous fluids." ACM Transactions on Graphics (TOG) 24.3 (2005): 915-920.
• Ng, Yen Ting, et al. "Guidelines for Poisson solvers on irregular domains with Dirichlet boundary conditions using the ghost fluid method." Journal of Scientific Computing 41.2 (2009): 300-320.
• Yang, Jianming, and Frederick Stern. "Sharp interface immersed-boundary/level-set method for wave–body interactions." Journal of Computational Physics 228.17 (2009): 6590-6616.

• Ervik, Åsmund, Karl Yngve Lervåg, and Svend Tollak Munkejord. "A robust method for calculating interface curvature and normal vectors using an extracted local level set." Journal of Computational Physics 257 (2014): 259-277.
• Lervåg, Karl Yngve, Bernhard Müller, and Svend Tollak Munkejord. "Calculation of the interface curvature and normal vector with the level-set method." Computers & Fluids 84 (2013): 218-230.
• Macklin, Paul, and John Lowengrub. "Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth." Journal of Computational Physics 203.1 (2005): 191-220.
• Macklin, Paul, and John S. Lowengrub. "A new ghost cell/level set method for moving boundary problems."