Generalized Riemann Problem and Nonlinear Wave Interactions in Macroscopic Production Model

ABSTRACT In this article, we examine a system of hyperbolic balance laws governing macroscopic production model which describes high‐volume product flows. Our primary focus is on the nonlinear wave interactions involving shock and rarefaction. Employing the theory of differential constraints, we first demonstrate that the governing system is compatible with a set of differential constraints, which allows us to handle the nonhomogeneous term by making the governing system diagonalized. We show that the governing system admits a strictly convex entropy–entropy flux pair which leads to the well‐posedness of the solution. Furthermore, we obtain the solution, that consists of shocks and rarefaction waves, of the Riemann problem as well as the generalized Riemann problem. Consequently, we discuss all possible interactions of elementary waves of the Riemann problem. Here, the primary challenge is to identify the solution structure of the generalized Riemann problem which is formed at the time of collision of shocks and rarefaction waves as solution of the Riemann problem. In addition, we implement an upwind‐based splitting scheme to validate the analytical results through various test cases.