The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model. (27th September 2021)

• Record Type: Journal Article
• Authors: Zhang, Yunfeng; Sun, Meina
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 2(2022)
• Page Start: 864
• Page End: 881
• Publication Date: 2021-09-27
• Subjects: delta shock wave -- macroscopic production model -- pressureless gas dynamics model -- Riemann problem -- vacuum state; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7818
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The exact solutions of the Riemann problems for the two different perturbed macroscopic production models are considered and constructed, respectively, for all the possible cases. It is found that the asymptotic limits of solutions to the Riemann problem for the first kind of perturbed macroscopic production model do not converge to those of the pressureless gas dynamics model, because the delta shock wave in the limiting situation has different propagation speed and strength from those for the pressureless gas dynamics model. In order to remedy it, the second kind of perturbed macroscopic production model is proposed, whose asymptotic limits of Riemann solutions are identical with those of the pressureless gas dynamics model.