Scalar one-dimensional and two-dimensional fluctuation splitting schemes will be discussed, together with the properties of the schemes, such as conservation, monotonicity and accuracy (linearity preservation). The ideas will be explained in one dimension for the linear advection equation, and consequently generalized to two dimensions. A linearization procedure for nonlinear advection equation is described, which is also applicable to systems of equations.
Results on test cases for steady-state are shown, as well as for the unsteady problems solved by other methods. Application to systems of equations is still much under research and will be addressed shortly.
For the entire collection see [Zbl 0788.00033].