# PDEs in their weak form in Comsol

If a physical model is not listed in the wizard, we can use Comsol's weak form to enter PDE's (governing equations of a system) in their weak form. How can it be done ?

for example: 2 equations of momentum (2D flow) coupled with continuity equation

$\rho \ v.\nabla v=-\nabla p +\mu \nabla^2 v$

$\nabla .v=0$

This model (well-known) is for calculating velocity and pressure fields

• I would assume that comsol manual to be of help here. Have you looked? Aug 10 '13 at 19:40
• unfortunately no, i don't have the manual. could u please give me a link for it(and also comsol documentation did not help). Aug 10 '13 at 20:35
• I don't know Comsol. What I meant to point out is that you are asking people to explain something that is already explained somewhere (the manual). This is not likely a successful strategy. Where did you get a copy of Comsol from that doesn't have a manual? And did you check online with the manufacturer whether they have a help page? Aug 10 '13 at 22:17
• Comsol solves the coupled pressure and velocity equations (NS equations) easily, waht i meant was to know if it is possible to solve the equatios using weak form or not. because i wanna simulate another model with 5 coupled PDE and i need to examine a simple one before the main project.and im not even able to solve simple NS equations using comsol. so i just need to know if it is possible or not.thanks. Aug 14 '13 at 9:57
• This document explains how to obtain the weak form of inductive heating equations that can be used in finite element softwares like COMSOL (Weak form interface). It gives the mathematical formulation of the problem and the weak form in vectoriel form and axisymmetric form. gum.co/XerZi Apr 11 '19 at 21:31

This "model" is the incompressible (constant density) Navier Stokes problem, the second equation being the mass balance: $$\frac{\partial\rho }{\partial t}+\nabla\cdot(\rho v)=0$$ I have worked in the past with Comsol, and I believe that the Navier Stokes weak forms are readily implemented in the CFD module as states the Comsol modeling manual in this LINK. You would only have to input the initial values of the (velocity,pressure) field and the boundary conditions. Your model input will be the density and the viscosity