UCSB CS 111 - Introduction to Scientific Computing Final Project 3 - Due on the ﬁnal exam day at 5pm You are not allowed to work in group for the ﬁnal project. The goal of this project is to implement the Navier-Stokes equations in two spatial dimensions. The velocity ﬁeld U = ( u,v ) is given by: U t + ( U · ∇ ) U =-∇ p + μ ∇ 2 U + F, with ∇ · U = 0 . Here p is the pressure, F = ( f 1 ,f 2 ) is an external force and μ = . 001 is the viscosity coeﬃcient. 1. What are the boundary conditions for the velocity at the walls? 2. Write down the main step of the projection method. 3. Write down the linear system associated with the discretization of the viscosity term. What are the boundary conditions? 4. Write down the linear system associated with imposing the incompressibility constraint. What
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Fundamental physics concepts, Computational fluid dynamics, projection method