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Total variation diminishing Runge-Kutta schemes
Open accessAbstract
In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total variation diminishing) spatial discretization, verifying the claim that TVD Runge-Kutta methods are important for such applications. We then explore the issue of optimal TVD Runge-Kutta methods for second, third and fourth order, and for low storage Runge-Kutta methods.
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Cited by
Shu, C.-W. (1998) · Lecture Notes in Mathematics · doi:10.1007/bfb0096355 · Cited by 1,919
Self-citationJohnstone, C. P., Güdel, M., Lammer, H., & Kislyakova, K. G. (2018) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201832776 · Cited by 97
“For each one of these updates, we use the 2nd order Total Variation Diminishing (TVD) Runge–Kutte scheme given by Gottlieb & Shu (1998), given by U(1) = Un + ∆t f (Un), (B.8) Un+1 = 1 2 ( Un + U(1) ) + 1 2 ∆t f (U(1)), (B.9) where f (Un) is ∂U/∂t calculated from Un.”
MethodMarangoni Effect in Bipropellant Droplet Mixing during Hypergolic Ignition
Sun, K., Jia, F., Zhang, P., Shu, L., & Wang, T. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.15.034076 · Cited by 16
Metadata
- Authors
- Gottlieb, S., & Shu, C.-W.
- Venue
- Mathematics of Computation
- Publisher
- American Mathematical Society (AMS)
- Published
- 1998
- Volume
- 67
- Issue
- 221
- Pages
- 73-85
- ISSN
- 0025-5718 (ISSN-L)
- 1088-6842
- OpenAlex
- W1969647398
- Cited by
- 2,527
- References
- 0
- FWCI
- 11.86
- Type
- journal article
- Language
- en
- Open access
- bronze
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