New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations

By Alexander Kurganov, Eitan Tadmor. 2000

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View Paper: https://www.semanticscholar.org/paper/190deb5b31a116733385d1185f872020e4b8d59c

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Citations in the corpus

A class of approximate Riemann solvers and their relation to relaxation schemes (2001, methodology): “We note in passing that the LxF and LLF methods can be extended to second-order accuracy to obtain the central schemes of Nessyahu & Tadmor [43] and Kurganov & Tadmor [30] respectively, and connections between these methods and relaxation schemes are briefly discussed in the introduction to [30].”
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations (2001, methodology): “In this way, a nonstaggered fully discrete central scheme is derived and is naturally reduced to a particularly simple semidiscrete form (for details see [26]).”
Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes (2006, background): “This amounts to using control volumes of width O(∆t) so that the resulting schemes admits semi-discrete limit as ∆t→0, the so called “central-upwind” schemes introduced in [22] and further generalized in [21].”
Operator splitting methods for degenerate convection–diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation (2000, methodology): “Kurganov and Tadmor [37] used an explicit embedded integration method with a large stability region.”
Analysis and numerical investigation of two dynamic models for liquid chromatography (2013, methodology): “In this paper, the local Lax–Friedrichs flux was used which satisfies the above mentioned properties, see e.g. Kurganov and Tadmor (2000), LeVeque (2003), Zhang and Liu (2005) hLLF ða,bÞ ¼ 1 2 ½f ða,gðaÞÞþ f ðb,gðbÞÞ Cðb aÞ , ð55Þ C ¼ max min ða,bÞr srmax ða,bÞ 9f 0ðs,gðsÞÞ9: ð56Þ The Gauss–Lobatto…”
On the treatment of entropy mixing in numerical cosmology (2008, methodology): “…using a Riemann solver for explicit shock capturing; it is also worth mentioning the characteristic-based Total Variation Diminishing scheme of Harten et al. (1987) and the characteristic-free scheme of Kurganov & Tadmor (2000) which achieve similar shock results without an explicit Riemann solver.”
Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications (2020, methodology): “In rhoCentralFoam, shock wave is accurately captured with the central-upwind Kurganov and Tadmor (KT) [20] or Kurganov, Noelle and Petrova (KNP) [21] scheme.”
A CENTRAL SCHEME FOR SHALLOW WATER FLOWS ALONG CHANNELS WITH IRREGULAR GEOMETRY (2009, unknown): “Semi-discrete central formulation We begin by describing the semi-discrete central scheme framework for approximating solutions for hyperbolic conservation laws (consult [15,16] for further details), vt + f(v)x = 0.”
New High-Resolution Semi-discrete Central Schemes for Hamilton—Jacobi Equations (2000, methodology): “These new schemes can be viewed as modifications of the central schemes of Lin and Tadmor (LT) [19, 20] and as an extension of the method developed by the authors in [ 15 ] for hyperbolic conservation laws and convection-diffusion equations.”
Solution of two‐dimensional Riemann problems for gas dynamics without Riemann problem solvers (2002, unknown): “In the more recent, less dissipative versions of central schemes presented in [14, 10, 12, 11, 13], staggered cells were placed in a distance of order O(∆t) from each other.”
CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM (2002, background): “Kurganov and Tadmor [21] introduced a new class of semi-discrete central schemes, which enjoy a much smaller numerical dissipation (∼ O((∆t)2r−1)).”
A review of numerical methods for nonlinear partial differential equations (2012, methodology): “(ii) To gain additional resolution, one can use nonoscillatory reconstruction of the missing numerical derivatives from the computed cell averages, yielding the Nessyahu–Tadmor scheme and its extensions [155, 126]:”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, unknown): “High-resolution Godunov-type semi-discrete centralupwind schemes, introduced in [13, 14] as a universal Riemann-problem-solver-free method for general multidimensional systems of hyperbolic conservation laws, satisfy the latter three requirements.”
CENTRAL SCHEMES AND CONTACT DISCONTINUITIES (2000, unknown): “Compared with the schemes from [13,14], the proposed schemes have smaller numerical viscosity, which leads to a sharper resolution of contact discontinuities.”