Weak local residuals as smoothness indicators for the shallow water equations

The system of shallow water equations admits infinitely many conservation laws. This paper investigates weak local residuals as smoothness indicators of numerical solutions to the shallowwater equations. To get a weak formulation, a test function and integration are introduced into the shallow water equations. We use a finite volume method to solve the shallow water equations numerically. Based on our numerical simulations, the weak local residual of a simple conservation lawwith a simple test function is identified to be the best as a smoothness indicator. © 2013 Elsevier Ltd. All rights reserved.