A detailed analysis is presented for the accuracy of several bounce-back methods for imposing no-slip walls in lattice-Boltzmann schemes. By solving the lattice-BGK (Bhatnagar-Gross-Krook) equations analytically in the case of plane Poiseuille flow, it is found that the volumetric approach by Chen et al. is first-order accurate in space, and the method of Bouzidi et al. second-order accurate in space. The latter method, however, is not mass conservative because of errors associated with interpolation of densities residing on grid nodes. Therefore, similar interpolations are applied to Chen's volumetric scheme, which indeed improves the accuracy in the case of plane Poiseuille flow with boundaries parallel to the underlying grid. For skew boundaries, however, it is found that the accuracy remains first order. An alternative volumetric approach is proposed with a more accurate description of the geometrical surface. This scheme is demonstrated to be second-order accurate, even in the case of skew channels. The scheme is mass conservative in the propagation step because of its volumetric description, but still not in the collision step. However, the deviation in the mass is, in general, found to be small and proportional to the second-order terms in the standard BGK equilibrium distribution. Consequently, the scheme is a priori mass conservative for Stokes flow.
The double Olympic champion has a talent for turning setbacks into chances for success. As he looks to make history in Paris, the Kenyan will be inspired by his comeback at the Tokyo Olympics following a disappointing 2020 London Marathon.
I use a Roku TV remote to navigate YouTube TV, and it lacks channel up and down buttons and a last-channel button. I've grown accustomed to not being able to flip through channels as I did with cable TV, but that's a behavior that decreased as I watched more shows on Netflix and Hulu anyway. Cable TV became more appointment viewing for sports and news than simply turning on the tube and blindly hunting around for something to watch.
Still, I miss the last button. I like being able to ping pong between two channels to avoid commercials. Sadly, there is no one-button solution to toggling back and forth between channels on YouTube TV. The fastest way I found involved four button presses:
The upside is that pressing the down arrow three times brings you to a row of thumbnails of the channels you've recently watched, which gives you more options than just the last channel you were on. The previous channel is always the left-most thumbnail.
This one took me weeks to figure out. YouTube TV has a semi-transparent guide overlay, and with no Exit button on my Roku TV remote, there's not an obvious way to exit out of the guide and get back to what you are watching. The Back button on the Roku remote brings up the guide, but it doesn't exit out of it as I would like it to. There's a three-button sequence you need to know to get rid of the guide and continue watching the current channel:
For this move, you'll need to log into your YouTube TV account on your computer or the YouTube TV mobile app. Head to Settings > Live guide. There you can drag to reorder the channels as they appear in the Live view of your channel guide. You can put your favorites at the top and can also deselect channels you don't watch to keep them from cluttering up your guide. It's a bit of a pain to drag channels manually that are located near the bottom of the guide to toward the top because you can only drag them so far at a time. A better way is to use the triple-dot button for your favorites and select Move to top and then drag them around once they are all located near the top of your guide.
Steelers seldom lose back-to-back, especially when the second is at home. Seattle needs more time to jell. To give up 429 yards to the Andy Dalton-led Bengals in Seattle? Watch for Pittsburgh rebound.
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