New answers tagged pde
3
Even if it is not completely physical in some computational FV codes like OpenFOAM exist something called "inletOutlet" boundary condition that make the speed 0 at the boundary when it assumes negative values (or opposite to the sign of your outlet condition). You can find an explanation here and here. Even if it can be a solution, I suggest you to ...
3
I know two papers that investigate infinite mapping layers and apply them to examples:
[1] Schoder, Stefan, et al. "Revisiting infinite mapping layer for open domain problems." Journal of computational physics 392 (2019): 354-367.
[2] Toth, Florian, Stefan Schoder, and Manfred Kaltenbacher. "An infinite mapping layer for deep water waves."...
3
You could use the following transformation
\begin{align}
&u = \tanh(x)\, ,\\
&v = \tanh(y)\, .
\end{align}
Another option is to use $2/\pi \arctan(x)$, but I have had better results with the hyperbolic tangent in the past.
1
Complementing Wolfgang answer, if you enumerate your nodes as $(0, 0), (1, 0), (0, 1), (\alpha_1, 0), (1 - \alpha_3, \alpha_3), (0, \alpha_2)$ you get the following basis functions:
\begin{align}
&\operatorname{N_{0}}{\left(x,y \right)} = 1 + \frac{y^{2}}{\alpha_{2}} + \frac{y \left(- \alpha_{2} - 1\right)}{\alpha_{2}} + \frac{x^{2}}{\alpha_{1}} + \frac{...
1
Almost all of the statements about the convergence of the finite element are only about the finite element space, not about what specific basis you choose for it. As a consequence, you are for example free to use an equidistant set of nodes to generate basis functions for the usual $P_k$ of $Q_k$ elements, or a set of nodes that correspond to Chebyshev or ...
4
We use domain decomposition because we want to exploit the power of more than one processor. As a consequence, the right question to pose is: "How do we need to partition the domain so that we get the maximal speedup by using as many processors as subdomains?"
The answer to that question is "subdomains need to be chosen so that the work ...
5
My first question: Will split ODE solvers likely work for my problem?
From your description, this sounds like a textbook use-case for a split ODE solver. Neither an implicit method nor an explicit method is practical across the entire ODE. IMEX methods sound like a reasonable choice as long as the atmospheric temperature dynamics that you want to treat ...
1
Anyone still interested in an answer, see this article:
P. Y. P. Chen and B. A. Malomed, "Lanczos-Chebyshev pseudospectral methods for wave-propagation problems," Mathematics Computers Simulation, vol. 82, no. 6, pp. 1056–1068, Feb. 2012.
In this published method, Crank-Nicholson forward difference method is used with an inner iterative step to ...
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