Boundary and initial condition

Boundary conditions and initial conditions dictate particular solutions to be obtained from Partial differential equations. Though the equations of fluid flow is same -Navier stokes equation but these boundary conditions actually drive the equations to actual solution. For example no slip condition at boundary, will lead to- u=v=w=0 at the surface or the initial wall temp is know= Tw, then boundary condition at wall will be T=Tw or for inviscid flow, flow slips over the surface, hence at surface/ boundary flow slips over surface:V ·n = 0.

Hence based on these boundary conditions, results are obtained.

These are of several types : 1. Inlet boundary conditions 2.Outlet boundary conditions 3.Wall boundary conditions 4.Symmetric bounday conditions etc.

But with types of P.D.E , boundary conditions also changes. For example

1. For elliptic equations: For solving such PDE, boundary conditions are required for the whole enclosed boundary.

2. For parabolic:( Marching type problem) The domain of solution for an parabolic PDE is an open Region. These are called Initial-Boundary value problems: Initial condition and two boundary conditions are required.

3, Hyperbolic: Initial boundary value problem: Two Initial conditions and two boundary conditions are required.

Hence It depends upon type of equation, if its elliptic then the boundary conditions for the whole enclosed boundary is required, for parabolic initial conditions are required etc.