Centred TVD schemes for hyperbolic conservation laws

By Eleuterio F. Toro, S. Billett. 2000

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MUSTA‐type upwind fluxes for non‐linear elasticity (2008, background): “and the two-step Lax–Wendroff flux FLW i+1/2(UL,UR, t, x)=F(ULW), ULW = 1 2 [UL + UR] − 1 2 t x [F(UR) − F(UL)] (13) Another, more recent, first-order centred flux is the FORCE flux [20, 21] given by the arithmetic average of the Lax–Friedrichs and Lax–Wendroff fluxes: Fforce i+1/2(UL,UR, t, x) = 1 ”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “Since the PRICE-T scheme [29] is the non-conservative analogue of the conservative FORCE scheme [31,32], that is in turn a deterministic re-interpretation of the staggered-grid version of the Random Choice Method (RCM) of Glimm [15], we briefly recall here the definition of the FORCE scheme for cons”
Finite-volume WENO schemes for three-dimensional conservation laws (2004, methodology): “The FORCE flux has been successfully used in the construction of centred multidimensional non-staggered mesh TVD schemes [ 27 , 28].”
Godunov-type methods for free-surface shallow flows: A review (2007, methodology): “A more accurate centred flux is the FORCE scheme (Toro and Billett, 1996, 2000).”