Recent content by hunt_mat

You can probably write a finite difference code easier than using comsol. Then you can insert the nonlinear part of the PDE with ease.

Okay.

The way you wrote Green's theorem is very odd. As you wrote it, it seems confused. It might be easier if you just wrote the normal \hat{\mathbf{n}}, and the flux, \mathbf{F}=(D,-C). It's I think that you've made an error with the signs of your normals. I'm using the finite volume method, so...

I am writing a 2D hydrocode in Lagrangian co-ordinates. I have never done this before, so I am completely clueless as to what I'm doing. I have a route as to what I want to do, but I don't know if this makes sense or not. I've gone from Eulerian to Lagrangian co-ordinates using the Piola...

I want to solve the following system of PDEs: \frac{\partial\nu}{\partial t}=\frac{\partial u}{\partial h} \frac{\partial u}{\partial t}=\frac{\partial}{\partial h}\left(f(\nu)\frac{\partial u}{\partial h}\right) I know the usual Fourier analysis that are applied to the stencil for single...

Are you talking about Navier's equations?

Let e^{i(x+y)}=e^{ix}e^{iy}=(\cos(x)+i\sin(x))(\cos(y)+i\sin(y)) Likewise for e^{i(x-y)}. Then add and subtract.

Try a transformation u=\tan^{-1}x. That should map everything onto a finite region.

My Courant number is 0.1. I should use: \frac{\partial v}{\partial x}\Bigg|_{x=x_{j}}\approx-\frac{3}{2\delta x}v_{j}+\frac{2}{\delta x}v_{j+1}-\frac{1}{2\delta x}v_{j+1} for my approximation?

I'm using a ``downwind'' approximation for the spatial derivative: \frac{\partial v}{\partial x}\approx -\frac{3}{2h}v_{j}+\frac{2}{h}v_{j-1}-\frac{1}{2h}v_{j-2} I'm using the usual approximation for the time derivative, I get the following for a stencil...

One of the ends is constrained and the other is free to move. I have a thermal poroelastic medium in which the porosity decreases as you heat up the bar. I don't need to model anything outside the bar.

I don't think it does to be honest, the system I'm modelling is essentially the thermal poroelestic system if that helps. I'm treating it as a continuum. As a base level, I require that no mass leaves or enters the system, so the mass flux should be zero at both ends should be zero, and that's...

Good question. On the free end, I would expect we can apply a stress-free condition as it's allowed to move. I'm not sure how this transfers to the density though.

Sorry, I didn't get back to this, there are three equations for \rho,u and T but the problem appears in the conservation of mass equation, so I thought that this would be the best equation to demonstrate the problem.

You're correct about the error in transformation, and I agree with your analysis at n'=0 but I am a little confused about your analysis, I did a similar analysis for the global conservation of mass. Like you I obtain: \frac{d}{dt}\int_{0}^{L(t)}\rho dx=0\Rightarrow...