# Tag Info

Accepted

### What kind of a researcher am I?

Up until a couple of decades ago, science was based on two large pillars. Those were theory and actual physical experiments. It is an exciting time to see a third pillar arise with numerical ...
• 2,935
Accepted

### Boundary condition for Pressure in Navier-Stokes equation

When we say that the pressure is only defined "up to a constant", what we mean is this: If $u,p$ is a solution to the Navier-Stokes equations, then $u,p+c$ for any constant $c$ is also a solution. In ...
• 55.5k

### Has a uniform estimate in k of the inf-sup constant for hp-DG methods for the Stokes problem been established?

The problem was solved recently: Lederer/SchÃ¶berl: Polynomial robust stability analysis for H(div)-conforming finite elements for the Stokes equations
• 1,124
Accepted

### Mixed Finite Element Method for the Stokes Systemâ€”Some Implementation Details

The topic of linear solvers for the Stokes equation is pretty well discussed in the literature, and the common consensus is that (i) using GMRES as the outer solver, (ii) the Silvester-Wathen approach ...
• 55.5k
Accepted

### Can we simulate compressible flows by simple direct explicit calculation, without solving systems of linear equations (such as Poisson eq)?

Physically, vorticity can only be created (as opposed to transported, stretched or intensified after being created) either by the appearance of a boundary layer on a solid surface, or through the ...
• 1,154
Accepted

### Projection method FVM poisson part, adding source term

The smooth solution turned out to have BC's applied in the following way: Walls and inlet: $\frac{\partial p}{\partial n}=0$ Outlet: $p=0$ Actually thought that we need only one value of P to pin, not ...
• 362
Accepted

### How do the navier stoke equations model materials who "forget" their original form?

The key difference between fluids and solids is that in a fluid, the stress is $$\nu \nabla \mathbf v,$$ (or some variation involving the symmetric gradient instead of the gradient) which involves ...
• 55.5k

### Why can the weak forms of the Stokes and continuity equations be combined into a single equation?

To get from weak form I to II, just add the two equations of weak form I. To see the other direction, note that weak form II has to hold for all test functions $\phi$ and $\psi$. That is, you can test ...
• 451

### Incompressible Navier-Stokes equations: Is projection method exact?

Note: I originally posted an answer that I was not 100% pleased with, so I have revised it heavily. 1/20/2017 The projection method is not in an exact approximation to the full system in general. ...
• 71
Accepted

### What is the difference between the curl component, and the divergence-free component, of a vector field?

@JannisTeunissen gave an answer for infinite domains. However, for finite domains, the Helmholtz decomposition is not unique, and the scalar potential $\phi$ can take many forms. First, it is true ...
• 55.5k
Accepted

### Galerkin method for a system of nonlinear PDEs

So first, represent your system as the following in your case: \begin{align} \frac{\partial q_k}{\partial t} - q_k \nabla \cdot F_k(\boldsymbol{q}) &= 0 & \forall k \in \lbrace 1, 2 \rbrace \...
• 4,248