This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such
examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate significant spurious oscillations, unless an extremely refined mesh is used. On the other hand, moving- water well-balanced methods perform well in these tests. The numerical examples in this note clearly demonstrate the importance of utilizing moving-water well-balanced methods for solutions near a moving-water equilibrium.
We discuss the thermodynamic properties of dark energy (DE) with Quintom matter in spinor scenario. (1).Using the Cardy-Verlinde formula, we investigate the conditions of validity of the Generalized Second Law of thermodynamics (GSL) in the four evol
utionary phases of Spinor Quintom-B model. We also clarify its relation with three cosmological entropy bounds. (2). We take thermodynamic stability of the combination between Spinor Quintom DE and the generalized Chaplygin Gas (GCG) perfect fluid into account, and we find that in the case of $beta>0$ and $0<T<T_0$, the system we consider is thermodynamically stable. (3) Making use of the Maxwell Relation and integrability condition, we derive all thermal quantities as functions of either entropy or volume, and present the relation with quantum perturbation stability.
