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The current scheme is a well-balanced method, which presents accurate and robust results in both steady and unsteady flow simulations.
We propose a simple well-balanced method named the slope selecting method which is efficient in both steady state capturing and preserving for hyperbolic system with geometrical source terms having concentrations.
Numerical tests show that the well-balanced method using an underlying numerical flux such as Lax Friedrichs flux, FORCE, GFORCE, or Roe fluxes can approximate very well the exact solution even when the initial data are on both supercritical region and subcritical region.
To capture this balance and near-equilibrium solutions, well-balanced methods have been introduced and performed well in many numerical tests.
In this chapter, we review some work on designing positivity-preserving and well-balanced methods for solving the shallow water equations with a nonflat bottom topography.
The implementation of this step is discussed in detail, as well as, the similarities and differences with some previous approaches to obtain well-balanced methods for the shallow water system.
Extensive one- and two-dimensional numerical examples are shown to demonstrate the performance of our well-balanced methods, and comparison with non-well-balanced results is included to illustrate the importance of maintaining the balance between pressure gradient and gravitational force numerically.
We complete a well-balanced numerical method by introducing computing correctors to an earlier scheme for a model of two-phase flows.
Using this method will result in a well balanced diet as well as a less bothered owner.
Well balanced and feels luxurious.
It's well balanced and very, very fun to drive.
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