Dissipation matrix and artificial heat conduction for Godunov‐type schemes of compressible fluid flows. (19th October 2016)

• Record Type: Journal Article
• Authors: Li, Jiequan; Tian, Baolin; Wang, Shuanghu
• Is Part Of: International journal for numerical methods in fluids. Volume 84:Number 2(2017)
• Page Start: 57
• Page End: 75
• Publication Date: 2016-10-19
• Subjects: Godunov scheme -- Riemann solvers -- dissipation matrix -- artificial heat conduction; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4340
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: This paper aims to reassess the Riemann solver for compressible fluid flows in Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov‐type schemes in the sense that associated dissipation matrix has zero determinant if an exact or approximate Riemann solver is used to construct numerical fluxes in the Lagrangian frame. This fact connects to some numerical defects such as the wall‐heating phenomenon and start‐up errors. To cure these numerical defects, a traditional numerical viscosity is added, as well as the artificial heat conduction is introduced via a simple passage of the Lax–Friedrichs type discretization of internal energy. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : This paper aims to reassess the Riemann solver for compressible fluid flows in the Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov‐type schemes in the Lagrangian frame, which connects to some numerical defects such as the wall‐heating phenomenon and start‐up errors. To cure the defects, the artificial heat conduction, in addition to the traditional numerical viscosity, is introduced via a passage of the Lax–Friedrichs type discretization of internal energy.