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6 votes

Modelling question: example of a physical phenomenon with this jump condition at an interface?

$\vec\Phi = K_i \nabla u_i$ is the flux across the interface. For example, if $u$ is the thermal energy density and $K$ the thermal conductivity, then $\vec\Phi$ is the thermal energy flux. Energy ...
Wolfgang Bangerth's user avatar
4 votes

Modelling question: example of a physical phenomenon with this jump condition at an interface?

In addition to Wolfgang Bangerth's explanation of temperature and concentration, let me give an other application where such interface conditions arise: (linear) elasticity, which has a similar ...
Zoltan Csati's user avatar
4 votes
Accepted

Methods of solving non-linear advection-diffusion systems beyond Newton-Raphson?

I'm assuming the limitation in 2D and 3D is storing the Jacobian. One option is to retain the time derivatives and use an explicit "pseudo" time-stepping to iterate to steady state. Normally the CFL ...
Aditya Kashi's user avatar
3 votes

ode45 with matrix initial conditions

You will need to write your problem such that the unknowns are a single vector, not a matrix. In your example with $N=2$, you will have an unknown vector $x(t)$ of size $20\times 1$ (not a matrix of $...
GertVdE's user avatar
  • 6,149
2 votes

How could we solve coupled PDE with finite difference method and Newton-Raphson method?

As mentioned by Matt Knepley, this is naturally formulated as a system of partial differential algebraic equations. Because you're in Matlab, you could consider doing the spatial discretization ...
muon's user avatar
  • 31
2 votes
Accepted

Implementing odespy for system of PDEs

Odespy needs from you a 1st order system of ODEs, namely something of the form \begin{align} \frac{d\mathbf{y}}{dt} = \mathbf{f}(\mathbf{y},t), \tag{1} \end{align} where, for your particular problem, ...
GoHokies's user avatar
  • 2,216
1 vote

Verification of coupled system of equations for light propagation

Use the Method of Manufactured Solutions to create whatever solution you like, crank it through the equations to give a forcing function and boundary conditions, and then put those into your solver ...
Bill Barth's user avatar
  • 10.9k
1 vote
Accepted

How to couple the vibro-acoustic equations by Mortar method for non-matching meshes?

After some digging I could finally find a paper that more or less answered my question: Bermúdez, A., Rodrıguez, R., & Santamarina, D. (2003). Finite element approximation of a displacement ...
Pepe's user avatar
  • 459
1 vote

Improving calculation algorithm for coupled PDEs

Given the dependency between $z$ and $t$, we can rewrite the first equation with a time derivative: $$\partial_tU=\frac{c}{n}\left(\nabla_r^2U+\rho U\right)$$. Now we define $g=\left(\begin{array}{c}...
Bort's user avatar
  • 1,285
1 vote

Numerical methods for coupled stiff PDEs

The first step is to add one more equation defined as: $$\frac{\partial y_3}{\partial t} = v$$ Then if you substitute equations 1 and 2 and the new equation into your modified equation 3 you get: $$...
Bill Greene's user avatar
  • 6,074
1 vote

Coupling Boundary Condition of one PDE with source term of another PDE

As written, it's not clear to me that it's actually fully coupled. That is, the solution to $B$ depends (via its BC2) on the solution to $a$, but assuming $\omega$ is simply some specified function of ...
muon's user avatar
  • 31
1 vote

Methods of solving non-linear advection-diffusion systems beyond Newton-Raphson?

From my experience with Navier-Stokes equations, one can do very well without fully implicit schemes. If you just want a fast numerical scheme for the solution of the time evolution, take a look at ...
Jan's user avatar
  • 3,418

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