Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:358

Article

Chertock, Alina¹  Cui, Shumo²  Kurganov, Alexander^3,4  Ozcan, Seyma Nur¹  Tadmor, Eitan⁵ 

[1] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

[3] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

[4] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[5] Univ Maryland, Dept Math, CSCAMM, IPST, College Pk, MD 20742 USA

关键词: Euler equations of gas dynamics with gravitation;    Well-balanced scheme;    Equilibrium variables;    Central-upwind scheme;    Piecewise linear reconstruction;   

DOI  :  10.1016/j.jcp.2017.12.026

来源: Elsevier

【 摘 要 】

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free