Numerical entropy production for shallow water flows

A numerical scheme for the entropy of the one dimensional shallow water wave equations is presented. The scheme follows from a well- balanced finite volume method for the quantity vector having water height and momentum as its components. The local truncation error of the entropy is called the numerical entropy production, and can be used to detect the location of a shock discontinuity. We show by numerical tests that the numerical entropy production performs better in detecting such a discontinuity than two local truncation errors of the numerical quantity.