A second-order, discretely well-balanced finite volume scheme for euler equations with gravity. (15th March 2019)

• Record Type: Journal Article
• Authors: Varma, Deepak; Chandrashekar, Praveen
• Is Part Of: Computers & fluids. Volume 181(2019)
• Page Start: 292
• Page End: 313
• Publication Date: 2019-03-15
• Subjects: Finite volume -- Euler equations -- Gravity -- Well-balanced; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2019.02.003
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Second order finite volume method admitting discrete hydrostatic solutions. Exploits structure of hydrostatic solution in reconstruction and source term. A priori knowledge of hydrostatic solution is not required. Well-balanced for any equation of state. Can be used with most standard numerical fluxes. Abstract: We present a well-balanced, second order, Godunov-type finite volume scheme for compressible Euler equations with gravity. By construction, the scheme admits a discrete stationary solution which is a second order accurate approximation to the exact stationary solution. Such a scheme is useful for problems involving complex equations of state and/or hydrostatic solutions which are not known in closed form expression. No á priori knowledge of the hydrostatic solution is required to achieve the well-balanced property. The performance of the scheme is demonstrated on several test cases in terms of preservation of hydrostatic solution and computation of small perturbations around a hydrostatic solution.