[AnasVFX]

I read Stable Fluids by Jos Stam and FLUID SIMULATION SIGGRAPH 2007 Course Notes by Robert Bridson. The boundary conditions in the two papers are different in my sight. I don't understand them. How are these two ways related to solving a linear system of PDEs with boundary conditions?

In Stam's paper, he uses a function called set_bnd to set boundaries, so is this function just setting the boundaries that I need in my matrix of linear systems of Pressure Poisson and Diffuse Equation? In Numerical Analysis, we don't modify the matrix with the boundary values, but we put the boundary condition either it's a Neumann or Dirichlet. I don't really understand what kind of boundaries is this set_bnd function. My thinking now is that it sets the boundary values which will be used to solve linear systems but what kind of boundaries?

In Bridson's paper, I don't find any implementation about boundaries except for speaking about the normal components of velocity. Actually, I can't find any relation between this and Stam's way. In the section on making fluid incompressible, he says something about boundaries but I don't understand. He just satisfies boundary conditions on the boundary cells then he solves the system or he put the boundaries in the matrix? Actually I don't know how to satisfy u*n = u_solid * n which I think is the no stick boundaries for interacting between a fluid and solid boundaries.