Axis-symmetrical Riemann problem solved with standard SPH method. Development of a polar formulation with artificial viscosity. (15th December 2017)

• Record Type: Journal Article
• Authors: Taddei, L.; Lebaal, N.; Roth, S.
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 12(2017)
• Page Start: 3161
• Page End: 3174
• Publication Date: 2017-12-15
• Subjects: Riemann problem -- SPH method -- Axis-symmetric -- Gaussian kernel -- Artificial viscosity; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.08.011
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper presents the development of a cylindrical SPH formulation based on previous study of the literature (Petschek et al) with an explicit formulation for the artificial viscosity. The entire development is explained to propose a formulation adapted to solve Euler equations in the case of a Riemann problem with axis-symmetric conditions. Thus, the artificial viscosity is constructed to find smooth solutions of well-known Riemann problems such as Sod, Noh and Sedov problems. Numerical results are compared to exact solutions and observations are made on numerical parameters influence. This study contributes to validate the axis-symmetrical formulation for pure hydrodynamics tests.