To Split or Not to Split, That Is the Question in Some Shallow Water   Equations
  In this paper we analyze the use of time splitting techniques for solving shallow water equation. We discuss some properties that these schemes should satisfy so that interactions between the source term and the shock waves are controlled. This paper shows that these schemes must be well balanced in the meaning expressed by Greenberg and Leroux [5]. More specifically, we analyze in what cases it is enough to verify an Approximate C-property and in which cases it is required to verify an Exact C-property (see [1], [2]). We also include some numerical tests in order to justify our reasoning. 
Vicente Mart\'inez
math.NA physics.flu-dyn