Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations

By Alexander Kurganov, Sebastian Noelle, Guergana Petrova. SIAM Journal on Scientific Computing, 2001

901 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/bb8d6924c298d748e69eacf6db85c94ba6ff416c

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Implementation of semi‐discrete, non‐staggered central schemes in a colocated, polyhedral, finite volume framework, for high‐speed viscous flows (2009, methodology): “The second-order semi-discrete, non-staggered schemes of KT [26] and Kurganov, Noelle and Petrova (KNP) [ 27 ] permit this.”
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].”
Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications (2020, methodology): “For KNP scheme, biasness is introduced in the upwind direction, depending on the onesided local speed of sound, leading to the central upwind characteristics of the KNP scheme.”
Central‐upwind schemes on triangular grids for hyperbolic systems of conservation laws (2005, methodology): “The derivation follows the approach from [8, 10 ]: we integrate over nonuniform polygonal control volumes of different shapes and derive a fully discrete central-upwind scheme.”
On the Reduction of Numerical Dissipation in Central-Upwind Schemes (2007, methodology): “For example, the least dissipative choice (fi = 0) corresponds to the original centralupwind scheme from [ 12 ].”
An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. Magnetohydrodynamics (2002, methodology): “This is why the HLL scheme described above was defined in Kurganov et al. (2001) as central-upwind.”
A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems (2002, methodology): “Then the semidiscrete central-upwind scheme can be written in the conservative form (see [ 9 ])”
CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM (2002, methodology): “This results in the central-upwind schemes [ 18 , 20].”
A CENTRAL SCHEME FOR SHALLOW WATER FLOWS ALONG CHANNELS WITH IRREGULAR GEOMETRY (2009, positive): “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.”
CENTRAL SCHEMES AND CONTACT DISCONTINUITIES (2000, methodology): “First, we would like to recall the construction of central-upwin d schemes (see [ 13 ]), which consist of three consecutive steps - reconstruction, evolution and projection back onto the original grid.”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, methodology): “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.”
Solution of two‐dimensional Riemann problems for gas dynamics without Riemann problem solvers (2002, positive): “In Section 2 we provide a brief description of the central schemes proposed in [ 11 ], which have been applied to the two-dimensional Euler equations of gas dynamics in Section 3. Compared with the ’simple’ 1-D congurations, the 2-D case oers 19 dierent congurations which consist of a considerably r”