Flux difference splitting and the balancing of source terms and flux gradients

By M. Hubbard, Pilar García-Navarro. 2000

282 citations recorded by the source corpus.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/8166ad0c0af5fee256421effbeffda9ed8230b1a

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In Computational Mechanics

1. Richard M. Iverson
2. Ioannis K. Nikolos
3. R. Denlinger
4. A. I. Delis
5. Sam S. Y. Wang
6. Xinya Ying
7. Azzeddine Soulaïmani
8. Y. Loukili

Citations in the corpus

• Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation (2004, methodology): “[27] We write the jumps in flux across each cell edge as a linear combination of right- and left-going waves and update the cell variables on either side as described by Hubbard and Garcia-Navarro [2000] and by LeVeque [2002, pp.”
• A novel multidimensional solution reconstruction and edge‐based limiting procedure for unstructured cell‐centered finite volumes with application to shallow water dynamics (2013, background): “As such, and following [3] and [9], a term, e ‰ , should be added to the source term discretization (right hand side of (27)) to maintain the correct balance.”
• High-order balanced CWENO scheme for movable bed shallow water equations (2007, methodology): “and the work by Hubbard and Garcia-Navarro [8], which analyzes the effects of source terms in a flux difference splitting technique, can be mentioned.”
• Numerical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF Approximation (2007, methodology): “For Roe’s scheme, certain methods appear to resolve this question by upwinding the discretization of the bed slope source term [42, 43].”
• A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography (2008, methodology): “This upwinding approach was extended to a wide range of problems by García-Navarro and Vázquez-Cendón [14], Bermúdez et al. [9] and Vázquez-Cendón [33].”
• Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows (2008, background): “3b), respectively, gives xL(Q ∗ − QL) = T(f L 2 − f ∗ 2 ) (13) xR(Q ∗ − QR) = T(f ∗ 2 − f R 2 ) (14) Substituting SL = −(xL/T) and SR = xR/T into Eqs (13) and (14), and then eliminating Q∗, we can obtain f ∗ 2 = SRf L 2 − SLf R 2 + SLSR(QR − QL) SR − SL (15)”
• A 2D numerical model of wave run-up and overtopping (2002, background): “Details can be found in Hubbard and Garcia-Navarro (2000).”