L2Roe: A low dissipation version of Roe’s approximate Riemann solver for low Mach numbers. 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.

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  1. Iampietro, D.; Daude, F.; Galon, P.: A low-diffusion self-adaptive flux-vector splitting approach for compressible flows (2020)
  2. Yu, Hang; Tian, Zhengyu; Yang, Fan; Li, Hua: On asymptotic behavior of HLL-type schemes at low Mach numbers (2020)
  3. Xie, Wenjia; Zhang, Ye; Chang, Qing; Li, Hua: Towards an accurate and robust Roe-type scheme for all Mach number flows (2019)
  4. Chen, Shu-sheng; Yan, Chao; Xiang, Xing-hao: Effective low-Mach number improvement for upwind schemes (2018)
  5. Simmonds, Nicholas; Tsoutsanis, Panagiotis; Antoniadis, Antonis F.; Jenkins, Karl W.; Gaylard, Adrian: Low-Mach number treatment for finite-volume schemes on unstructured meshes (2018)
  6. Barsukow, Wasilij; Edelmann, Philipp V. F.; Klingenberg, Christian; Miczek, Fabian; Röpke, Friedrich K.: A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics (2017)
  7. Flad, David; Gassner, Gregor: On the use of kinetic energy preserving DG-schemes for large eddy simulation (2017)
  8. Blom, David S.; Birken, Philipp; Bijl, Hester; Kessels, Fleur; Meister, Andreas; van Zuijlen, Alexander H.: A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows (2016)
  9. Dellacherie, S.; Jung, J.; Omnes, P.; Raviart, P.-A.: Construction of modified Godunov-type schemes accurate at any Mach number for the compressible Euler system (2016)
  10. Mor-Yossef, Y.: AUFSR+: low Mach number enhancement of the AUFSR scheme (2016)