Weak Form for Navier-Stokes with Chorin's Projection

In order to solve the equations of fluid motion with FEniCS, we need to translate the Partial Differential Equations (PDEs) into their weak form together with a method to enforce incompressibility. Here are the notes: https://github.com/Ceyron/machine-lea... The Navier-Stokes equations are the fundamental description for fluid mechanics. They are notoriously hard to solve numerically due to their saddle point structure by the incompressibility constraint. A Finite Element discretization by the FEniCS Python library requires a translation of the strong form into the weak form. In order to do so, we, however, first have to apply a projection method to enforce incompressibility given by the 2nd PDE. We will do this in strong form and then get a three-step algorithm for solving the Navier-Stokes equations. Finally, we have to translate all three strong PDEs into their weak form. This process involves the reverse product rule and an application of Gauss/Divergence theorem. All steps are presented in detail ;). ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-lea... 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff:   / felix-koehler   and   / felix_m_koehler   💸 : If you want to support my work on the channel, you can become a Patreon here:   / mlsim   ------- Timestamps: 00:00 Intro 00:55 BC & IC for specific example 01:53 Agenda 02:13 Chorin's Projection overview (an operator splitting) 05:01 An algorithm in strong form 09:02 Obtaining an equation for pressure 13:23 Summary in strong form 15:41 (1) Weak form for tentative momentum step 30:11 (2) Weak form for Pressure Poisson problem 33:37 (3) Weak form for Velocity Projection/Correction 36:13 Summary in weak form 40:37 Outro