Internal generation of damped waves in linear shallow water equations

Techniques to generate damped waves in linear shallow water equations are developed. Delta-shaped source functions are derived for four different cases with the source function and damping coefficient either in the continuity or momentum equation. Source terms are also found by relating the source function method to the source term addition method. For the transport of the source term in damped waves, we define complex valued source-term velocity which is different from the real valued energy velocity. We verify the present wave generation techniques with the source-term velocity by simulating damped waves on a horizontal bottom both in the one- and two-dimensional domains, and also damped waves shoaling and refracting on a plane slope in the two-dimensional domain.