Regarding the numerical stabilization of two-dimensional advection equation,\begin{equation}\dfrac{\partial f}{\partial t} + \Big(\dfrac{d\varepsilon_1(k)}{dk}\Big)\dfrac{\partial f}{\partial z}- \Big( \dfrac{d\varepsilon_2(z)}{dz} \Big)\dfrac{\partial f}{\partial k} = 0\end{equation}I have encountered some texts that propose using entropy functions. For example, it is mentioned that the choice of \begin{equation}h(f,z,k) = fe^{\varepsilon_1+\varepsilon_2}\end{equation}will do the job for the above equation.How is the given function (or any other entropy function) increasing the numerical stability? What is the main idea behind using such functions?
Using entropy functions for increasing numerical stability
pde;stability;hyperbolic pde;numerical