The selective control feature for physically accurate solutions of all variables and application in first order linear transient hyperbolic systems

The objective in this paper is to extend the previously developed twoparameter GS4-1 (Generalized Single System Single Solve for 1st order transient systems) computational framework from parabolic to hyperbolic type of applications pertaining to first order linear transient systems. In particular, attention is paid to the selective control feature inherit in the framework, which is the new feature that enables different amounts of high frequency damping for the primary variable and its time derivative, allowing for physically accurate solutions of all variables in the system. This is in contrast to having only limited, often indiscriminate, control of the high frequency damping on these variables which may not be sufficient to suppress the numerical oscillations in the time derivative variable.