Timeline for CFL condition and Lax-Friedrich numerical flux
Current License: CC BY-SA 3.0
14 events
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| Jan 31, 2023 at 22:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 3, 2022 at 22:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 5, 2022 at 21:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 5, 2022 at 20:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 6, 2022 at 18:07 | answer | added | Dan Doe | timeline score: 1 | |
| Jan 18, 2015 at 6:30 | comment | added | Pranav | I had solved the same problem over an year ago. If I remember correctly, $\alpha$ is the max eigenvalue of the system at the "face" between two nodes (as it is being used to compute the flux). Hence you will have 4 combinations of $u\pm\sqrt{gh}$, considering velocities of nodes on both sides of the face, and then take max $\lambda$ of these 4 eigenvalues. | |
| Jan 17, 2015 at 22:48 | comment | added | Kyle Mandli | Yeah, that's the gist of it. Basically we choose the wave speeds to form a numerical cone of dependence such that all of the waves are contained inside of the numerical cone. | |
| Jan 17, 2015 at 12:40 | comment | added | BRabbit27 | Assuming the max wave speed computed previously is correct, I can also use that value for $\alpha$ in the Lax-Friedrichs numerical flux? | |
| Jan 17, 2015 at 12:39 | comment | added | BRabbit27 | For a system, the wave speeds are given by the eigenvalues of the flux matrix. These are $m/h ± \sqrt{gh}$. So from my solution vector $Q$ compute $\lambda_1$ and $\lambda_2$, which are also vectors, then I just take the max(max(\lambda_1,\lambda_2)) and with that speed I can calculate the time step $\Delta t = \frac{\Delta x}{maxSpeed}$, is this correct? | |
| Jan 17, 2015 at 12:31 | history | undeleted | BRabbit27 | ||
| Jan 17, 2015 at 12:30 | history | deleted | BRabbit27 | via Vote | |
| Jan 16, 2015 at 20:56 | comment | added | Kyle Mandli | My guess is that you have a bit of notation confusion. In the second equation $w$ probably represents the vector of quantities of interest (evaluate the flux function at the state w) and in the fourth $|u|$ is the velocity of the flow and $c$ the gravity wave speed $\sqrt{g h}$ given that the document you referred to on the shallow water equations. For the other question regarding CFL conditions of systems one usually considers the maximum of the wave speeds of the system (in either direction). | |
| Jan 16, 2015 at 17:11 | history | edited | BRabbit27 | CC BY-SA 3.0 |
added 274 characters in body
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| Jan 16, 2015 at 16:58 | history | asked | BRabbit27 | CC BY-SA 3.0 |