Recent content by Niles

Homework Statement I have a range of numbers numbers n_i, each with a different weight w_i that sum up to 1. To keep things simple, let's take the case where we have three numbers with the following weights: n_i w_i ------------------------------...

Homework Statement I am looking at the following system: It shows a pore/tube (B) which is attached to a reservoir A. The fluid in reservoir A has a non-zero velocity in the horizontal direction, but I assume that the tube B is so long that the velocity there is unaffected and still zero...

It is on a rectangular 2D grid, grid points equally spaced. It is a simulated velocity field, so it obeys continuity. I don't know any of the streamlines by default

Homework Statement I have a discrete two-dimensional velocity field (u,v). I want to plot the streamlines by finding the streamfunction ψ and from that plot the streamlines by finding the curves where ψ=constant.Homework Equations In order to find ψ I then have to solve the equations (see link)...

Thanks, that is also what I thought. But then my matrix has dimensions 10x10, but my field will have 11 values since x_11 and x_1 are not the same. But that won't work when I multiply them together (?) Am I missing something?

I am trying to set up the mass matrix for a 1D system which I want to solve using finite elements. So the mass matrix is defined as M = \int{NN^T}dL, where N is the finite element linear basis functions. I use hat functions. Say I have 10 elements, corresponding to 11 nodes running from -5...

Homework Statement Hi Is there a rigorous way to find conformal mappins? Say I would like to find how \phi(z)=z^{0.5} maps the domain r\exp(i\phi) (with r>0 and 0\leq \phi \leq \pi), how would I do this? Thanks in advance.

Homework Statement Hi The stream function for a cylinder with radius a in a uniform crosswind is given by (https://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder#Stream_function) \psi = Ur \sin(1-a^2/r^2) How does one show this formally?

Homework Statement The Euler equations for ideal compressible flow are given by \partial_t v + (v\cdot \nabla)v = g-\frac{1}{\rho}\nabla p \\ \partial_t \rho + \nabla \cdot(\rho v) = 0 In my book these are written in terms of the small-value expansions \rho = \rho_0 + \delta \rho, p = p_0 +...

Thanks. I hope there is omething else you can help me with (you seem to have experience with this kind of notation). Is the following always true for some vector u? \nabla \cdot (\nabla u) = \nabla (\nabla \cdot u)

Homework Statement Hi I have a vector v. According to my book, the following is valid: \frac{1}{2}\nabla v^2-v\cdot \nabla v = v\times \nabla \times v I disagree with this, because the first term on the LHS I can write as (partial differentiation) \frac{1}{2}\partial_i v_jv_j =...

Hi In my lecture notes we making some calculations and all terms \mathcal O(M^3) are to be thrown away. Here M is the Mach number. Now, there is the expression (u denotes the velocity): uu\partial_t \rho \approx \rho_0 uu\nabla u which in my notes are thrown away because they claim it is...

Hi HallsofIvy Thanks, I remember that. But the RHS is in terms of a rotation operatir, not the gradient as I have.

Homework Statement I have the following integral \int_{ABC}{\mathbf{v}\cdot \nabla f_id\sigma} where $d\sigma$ is an area element, $\mathbf v$ is a velocity vector and f_i some function. The integral is performed across a triangle ABC and it is assumed that f is linear. In my book this...

Thanks for the help so far, both of you. That is exactly how it is used in my case (a Chapman-Enskog expansion). But doesn't this require that the various terms f_n are somewhat independent, so we can solve for each order independently?