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L2Roe: A low-dissipation version of Roe's approximate Riemann solver for low Mach numbers

Osswald, Kai; Siegmund, Alexander; Birken, Philipp LU ; Hannemann, Volker and Meister, Andreas (2015) In International Journal for Numerical Methods in Fluids
Abstract
A modification of the Roe scheme called L2Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the... (More)
A modification of the Roe scheme called L2Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M∞=0.001) to hypersonic (M∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L2Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Riemann solvers, finite volume methods, low mach, asymptotic analysis, numerical dissipation
in
International Journal for Numerical Methods in Fluids
publisher
John Wiley & Sons
external identifiers
  • scopus:84945380019
  • wos:000374344700001
ISSN
1097-0363
DOI
10.1002/fld.4175
language
English
LU publication?
yes
id
b0952dd2-babe-42bf-8163-2ba0dc4eefba (old id 8146348)
date added to LUP
2015-11-11 14:25:46
date last changed
2017-11-12 03:07:00
@article{b0952dd2-babe-42bf-8163-2ba0dc4eefba,
  abstract     = {A modification of the Roe scheme called L2Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M∞=0.001) to hypersonic (M∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L2Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases.},
  author       = {Osswald, Kai and Siegmund, Alexander and Birken, Philipp and Hannemann, Volker and Meister, Andreas},
  issn         = {1097-0363},
  keyword      = {Riemann solvers,finite volume methods,low mach,asymptotic analysis,numerical dissipation},
  language     = {eng},
  month        = {09},
  publisher    = {John Wiley & Sons},
  series       = {International Journal for Numerical Methods in Fluids},
  title        = {L2Roe: A low-dissipation version of Roe's approximate Riemann solver for low Mach numbers},
  url          = {http://dx.doi.org/10.1002/fld.4175},
  year         = {2015},
}