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Overview: At high Mach numbers the two-dimensional time-developing mixing layer develops shock waves, positioned around large-scale vortical structures. A suitable numerical method has to be able to capture the inherent instability of the flow, leading to the roll-up of vortices, and also must be able to capture shock waves when they develop. Standard schemes for low speed turbulent flows, for example spectral methods, rely on resolution of all flow-features and cannot handle shock waves, which become too thin at any realistic Reynolds number. The performance of a class of second-order explicit total variation diminishing (TVD) schemes on a compressible mixing layer problem was studied. The basic idea is to capture the physics of the flow correctly, by resolving down to the smallest turbulent length scales, without resorting to turbulence or sub-grid scale modeling, and at the same time capture shock waves without spurious oscillations. The present study indicates that TVD schemes can capture the shocks accurately when they form, but (without resorting to a finer grid) have poor accuracy in computing the vortex growth. The solution accuracy depends on the choice of limiter. However a larger number of grid points are in general required to resolve the correct vortex growth. The low accuracy in computing time-dependent problems containing shock waves as well as vortical structures is partly due to the inherent shock-capturing property of all TVD schemes. In order to capture shock waves without spurious oscillations these schemes reduce to first-order near extrema and indirectly produce clipping phenomena, leading to inaccuracy in the computation of vortex growth. Accurate simulation of unsteady turbulent fluid flows with shock waves will require further development of efficient, uniformly higher than second-order accurate, shock-capturing methods. Sandham, N. D. and Yee, H. C. Ames Research Center NASA-TM-102194, A-89139, NAS 1.15:102194 ...
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National Aeronautics and Space Administration is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, National Aeronautics and Space Administration can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.
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Finished it in a couple of days. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Would probably read it again at some point.
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Finished it in a couple of days. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Would probably read it again at some point.
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Glad someone recommended this to me. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Glad I picked this up.
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I have mixed feelings about this one. The pacing was a bit slow and I found myself skimming a few pages. It wasn't terrible, just okay. Might work better for someone else, just wasn't completely for me.
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Sharon WhiteOctober 24, 2025
An average read for me. It had some good moments, but the overall plot felt a bit disjointed in the second half. Might work better for someone else, just wasn't completely for me.
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I have mixed feelings about this one. Some parts were interesting, while others were a bit of a slog to get through. A generous 3 stars.
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A very satisfying read. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Would probably read it again at some point.
Deborah ScottMay 23, 2024
Finished it in a couple of days. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Glad I picked this up.
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It was okay. The pacing was a bit slow and I found myself skimming a few pages. It wasn't terrible, just okay. Probably won't read it again, but it was an okay way to pass the time.
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I liked it for the most part. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Enjoyable weekend read.
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A solid read. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Enjoyable weekend read.
Joseph WalkerMay 03, 2025
An average read for me. The writing was fine, but I didn't feel very connected to the characters. They felt a bit flat. It's fine if you have nothing else to read.
Patricia GonzalezJanuary 14, 2024
A very satisfying read. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. A solid 5/5 for me.
Deborah HallJuly 13, 2024
A solid read. It held my attention, even if a few things were a little predictable. A solid 4 stars from me.
Barbara BakerOctober 11, 2024
Really enjoyed this one. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Glad I picked this up.
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It was okay. The pacing was a bit slow and I found myself skimming a few pages. It wasn't terrible, just okay. Probably won't read it again, but it was an okay way to pass the time.
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Finished it in a couple of days. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Would probably read it again at some point.
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Not bad, but not my favorite. Some parts were interesting, while others were a bit of a slog to get through. Just right down the middle.
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Really enjoyed this one. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Will be looking for more from this author.
Anthony MillerJuly 24, 2024
Honestly one of the better books I've read lately. I got really invested in the main character's journey. Everything just clicked for me. Will be looking for more from this author.
Nicholas RobinsonMay 11, 2025
It was just alright. It felt a bit repetitive in the middle. Could have been shorter. It's fine if you have nothing else to read.
Kimberly SmithAugust 08, 2024
Glad someone recommended this to me. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Worth the time and money.
Steven PhillipsJune 02, 2025
I liked it for the most part. Interesting premise and executed fairly well. Just a few slow chapters here and there. Still a good book.
Elizabeth WalkerNovember 05, 2025
Took me a few chapters to get into it, but it was worth it. The middle dragged a tiny bit, but the ending totally made up for it. Enjoyable weekend read.
Carol ThompsonDecember 11, 2025
A very satisfying read. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Will be looking for more from this author.
Elizabeth PhillipsJuly 06, 2025
Such a great read. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Glad I picked this up.
Patricia CarterNovember 16, 2025
I have mixed feelings about this one. It had some good moments, but the overall plot felt a bit disjointed in the second half. Just right down the middle.
Barbara WrightDecember 30, 2025
I liked it for the most part. Interesting premise and executed fairly well. Just a few slow chapters here and there. Enjoyable weekend read.
Cynthia LeeJuly 19, 2025
Glad someone recommended this to me. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Definitely recommend it if you like this genre.
Susan MartinAugust 29, 2024
Really enjoyed this one. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Will be looking for more from this author.
Daniel RiveraDecember 03, 2025
Finished it in a couple of days. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Will be looking for more from this author.
Michael LewisAugust 15, 2024
Good, but not quite perfect. Interesting premise and executed fairly well. Just a few slow chapters here and there. I'd probably recommend it to a friend.
James TorresNovember 09, 2025
I was pleasantly surprised. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Worth the time and money.
Laura AdamsJune 03, 2024
Such a great read. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Definitely recommend it if you like this genre.
Christopher RiveraJune 15, 2024
Pretty good overall. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Still a good book.
Susan RodriguezNovember 12, 2024
I liked it for the most part. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Enjoyable weekend read.
Lisa GonzalezMarch 15, 2025
Glad someone recommended this to me. I got really invested in the main character's journey. Everything just clicked for me. Worth the time and money.
Sharon TaylorMarch 14, 2025
Pretty good overall. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. I'd probably recommend it to a friend.
Joshua ScottMay 04, 2024
I liked it for the most part. I liked the main character, though some of the side plots were just okay. A solid 4 stars from me.
Gary KingJune 06, 2024
I was pleasantly surprised. I got really invested in the main character's journey. Everything just clicked for me. Will be looking for more from this author.
Linda GreenFebruary 06, 2024
Really enjoyed this one. I got really invested in the main character's journey. Everything just clicked for me. Will be looking for more from this author.
George NguyenMarch 30, 2024
Good, but not quite perfect. Interesting premise and executed fairly well. Just a few slow chapters here and there. A solid 4 stars from me.
Ryan RiveraMay 30, 2025
A solid read. The middle dragged a tiny bit, but the ending totally made up for it. Still a good book.
Donald LeeJanuary 04, 2025
It was just alright. The writing was fine, but I didn't feel very connected to the characters. They felt a bit flat. A generous 3 stars.
Paul LeeApril 08, 2024
A solid read. I liked the main character, though some of the side plots were just okay. Enjoyable weekend read.
Deborah HallApril 11, 2024
I liked it for the most part. It held my attention, even if a few things were a little predictable. I'd probably recommend it to a friend.
Susan LewisFebruary 08, 2024
Honestly one of the better books I've read lately. I got really invested in the main character's journey. Everything just clicked for me. Glad I picked this up.
Jennifer CampbellOctober 25, 2025
A very satisfying read. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Worth the time and money.
Jacob ScottMay 17, 2025
Took me a few chapters to get into it, but it was worth it. It held my attention, even if a few things were a little predictable. Not bad at all.
Nicholas ClarkJune 16, 2025
Really enjoyed this one. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Will be looking for more from this author.
Carol ClarkNovember 21, 2025
It was just alright. The pacing was a bit slow and I found myself skimming a few pages. It wasn't terrible, just okay. A generous 3 stars.
Cynthia WilsonSeptember 19, 2025
Took me a few chapters to get into it, but it was worth it. I liked the main character, though some of the side plots were just okay. A solid 4 stars from me.
William CampbellMay 15, 2024
I was pleasantly surprised. I got really invested in the main character's journey. Everything just clicked for me. Definitely recommend it if you like this genre.
Donald BrownJuly 17, 2025
I liked it for the most part. Interesting premise and executed fairly well. Just a few slow chapters here and there. Not bad at all.
Ryan GarciaAugust 11, 2024
It was just alright. It had some good moments, but the overall plot felt a bit disjointed in the second half. Just right down the middle.
Cynthia AndersonMay 18, 2024
An average read for me. It felt a bit repetitive in the middle. Could have been shorter. A generous 3 stars.
Donald WrightMarch 04, 2024
I was pleasantly surprised. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Worth the time and money.
Carol DiazNovember 24, 2025
Honestly one of the better books I've read lately. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Would probably read it again at some point.
Jacob ThompsonMay 04, 2025
A solid read. Writing is good, just wish there was a bit more depth in certain parts. Still kept my attention though. Still a good book.
William CarterOctober 22, 2025
Glad someone recommended this to me. I got really invested in the main character's journey. Everything just clicked for me. Definitely recommend it if you like this genre.
Melissa WhiteJuly 05, 2024
A solid read. I liked the main character, though some of the side plots were just okay. Still a good book.
Ryan KingJuly 06, 2025
Took me a few chapters to get into it, but it was worth it. The middle dragged a tiny bit, but the ending totally made up for it. Enjoyable weekend read.
Andrew CruzDecember 08, 2025
Honestly one of the better books I've read lately. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Would probably read it again at some point.
Ryan WilliamsAugust 30, 2025
Finished it in a couple of days. The author did a great job wrapping everything up at the end. No weird plot holes left behind. A solid 5/5 for me.
Deborah CruzJuly 12, 2024
Really enjoyed this one. I got really invested in the main character's journey. Everything just clicked for me. Will be looking for more from this author.
Melissa CruzOctober 22, 2024
Really enjoyed this one. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. A solid 5/5 for me.
Robert EdwardsDecember 29, 2024
Such a great read. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Glad I picked this up.
Jessica PhillipsSeptember 24, 2024
Honestly one of the better books I've read lately. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Glad I picked this up.
Mark EvansJanuary 05, 2025
Honestly one of the better books I've read lately. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. A solid 5/5 for me.
Melissa CruzJune 03, 2024
Glad someone recommended this to me. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Definitely recommend it if you like this genre.
Susan RodriguezJuly 12, 2024
Such a great read. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. A solid 5/5 for me.
Paul LeeJanuary 09, 2024
A solid read. I liked the main character, though some of the side plots were just okay. Still a good book.
Nicholas CollinsJune 23, 2025
Honestly one of the better books I've read lately. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Worth the time and money.
Deborah CruzAugust 13, 2024
I have mixed feelings about this one. It had some good moments, but the overall plot felt a bit disjointed in the second half. It's fine if you have nothing else to read.
Sharon TaylorJanuary 15, 2025
A very satisfying read. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Definitely recommend it if you like this genre.
Kimberly LewisFebruary 26, 2024
Pretty good overall. The middle dragged a tiny bit, but the ending totally made up for it. Not bad at all.
Eric YoungOctober 30, 2024
Really enjoyed this one. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Definitely recommend it if you like this genre.
Stephanie BakerAugust 20, 2025
Really enjoyed this one. The author did a great job wrapping everything up at the end. No weird plot holes left behind. Glad I picked this up.
Robert EvansJune 25, 2025
A solid read. The middle dragged a tiny bit, but the ending totally made up for it. Still a good book.
Jessica LopezJanuary 03, 2024
Finished it in a couple of days. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Will be looking for more from this author.
David DavisSeptember 11, 2025
A very satisfying read. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. Worth the time and money.
Susan LeeAugust 06, 2024
Finished it in a couple of days. I loved how the story unfolded. It kept me guessing without being too confusing. Will be looking for more from this author.
Patricia CampbellApril 29, 2024
I have mixed feelings about this one. It had some good moments, but the overall plot felt a bit disjointed in the second half. Just right down the middle.
Charles WhiteMarch 28, 2025
Such a great read. The pacing was spot on and the characters felt real. I didn't find myself getting bored at any point. A solid 5/5 for me.
Charles ThomasJune 17, 2025
Honestly one of the better books I've read lately. It has a good balance of dialogue and description. Everything felt like it moved at the right speed. Glad I picked this up.
Linda JacksonOctober 28, 2024
Honestly one of the better books I've read lately. I got really invested in the main character's journey. Everything just clicked for me. Worth the time and money.
Anthony MitchellFebruary 26, 2024
An average read for me. The pacing was a bit slow and I found myself skimming a few pages. It wasn't terrible, just okay. It's fine if you have nothing else to read.
Nicholas KingMay 30, 2024
A solid read. I liked the main character, though some of the side plots were just okay. Enjoyable weekend read.
James TorresAugust 01, 2025
Really enjoyed this one. I got really invested in the main character's journey. Everything just clicked for me. Worth the time and money.
Nicholas YoungAugust 29, 2024
I was pleasantly surprised. I got really invested in the main character's journey. Everything just clicked for me. Worth the time and money.
Melissa RobertsOctober 29, 2025
I was pleasantly surprised. I got really invested in the main character's journey. Everything just clicked for me. Would probably read it again at some point.
Mary HallJune 11, 2025
Honestly one of the better books I've read lately. I loved how the story unfolded. It kept me guessing without being too confusing. Will be looking for more from this author.
Amanda RobinsonAugust 30, 2025
Finished it in a couple of days. I loved how the story unfolded. It kept me guessing without being too confusing. A solid 5/5 for me.
Robert EdwardsAugust 24, 2025
I was pleasantly surprised. I got really invested in the main character's journey. Everything just clicked for me. Glad I picked this up.
Melissa AndersonAugust 07, 2024
A very satisfying read. The writing style is very engaging. It’s easy to follow but still has a lot of depth. Glad I picked this up.