Reprint of: Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates. (30th June 2018)

• Record Type: Journal Article
• Authors: Ling, Dan; Cheng, Juan; Shu, Chi-Wang
• Is Part Of: Computers & fluids. Volume 169(2018)
• Page Start: 230
• Page End: 248
• Publication Date: 2018-06-30
• Subjects: Lagrangian method -- Cylindrical coordinates -- Symmetry-preserving -- Positivity-preserving -- Compressible flows; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2018.03.049
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: A high order positivity-preserving Lagrangian scheme in 1D cylindrical coordinate is developed. A 2D second order symmetry-preserving and positivity-preserving Lagrangian scheme is developed. Demanding 1D and 2D numerical tests are used to demonstrate the good performance of these schemes. Abstract: For a Lagrangian scheme solving the compressible Euler equations in cylindrical coordinates, two important issues are whether the scheme can maintain spherical symmetry (symmetry-preserving) and whether the scheme can maintain positivity of density and internal energy (positivity-preserving). While there were previous results in the literature either for symmetry-preserving in the cylindrical coordinates or for positivity-preserving in cartesian coordinates, the design of a Lagrangian scheme in cylindrical coordinates, which is high order in one-dimension and second order in two-dimensions, and can maintain both spherical symmetry-preservation and positivity-preservation simultaneously, is challenging. In this paper we design such a Lagrangian scheme and provide numerical results to demonstrate its good behavior.