Author(s)

Abhishek Kundu ¹, Arnab Basu ²

Affiliation(s)

¹ Department of Mechanical Engineering, Institute of Engineering & Management, Kol-700091
² Department of Basic Science & Humanities, Institute of Engineering & Management, Kol-700091

Corresponding Author

Abhishek Kundu

ABSTRACT

We present a class of third-order upwind compact schemes and develop an implementation strategy for un-steady compressible flow applications with strong shocks and vortices. Two adjustable parameters are left for the user to tune the scheme for specific applications. A third-order upwind scheme reported by Tolstykh and termed CUD-3 (High accuracy non-central compact difference schemes for fluid dynamic applications, World Scientific) turns out to be a particular case of the presented class of schemes. The aforementioned adjustable parameters allow us to derive schemes that perform better than the CUD-3. A large number of compressible solvers in use today for applications involving sharp gradients in the flow field employs flux limiters. We pose our compact scheme as a cell-face variable interpolation scheme so that available limiters may be applied during construction of the cell-face fluxes. Solvers based on popular schemes such as the AUSM class of schemes or the CUSP will require minimal modification to incorporate the proposed flux reconstruction method using compact upwinding. A number of test cases in one dimensions are then solved to show the usefulness of the proposed scheme and its implementation strategy.

KEYWORDS

Compact upwind scheme, CUD3, MUSCL, Euler equations

CITE THIS PAPER

Abhishek Kundu, Arnab Basu, A Class of Third-Order Compact Upwind Schemes for Compressible Flow with Shocks and Vortices, Journal of Physics Through Computation (2019) Vol. 2: 1-5. DOI: http://dx.doi.org/10.23977/jptc.2019.21001.

REFERENCES

[1] Tolstykh, A.I. (1994) High-accuracy non-centered compact difference schemes for fluid dynamics applications. World Scientific.
[2] Hirsh, R.S. (1975) High order accurate difference solutions of fluid mechanics problems by a compact differencing technique. J. Comput. Phys., 19, 90-109.
[3] Lele, S. (1992) Compact finite difference schemes with spectral-like resolution. J. Comput. Phys., 103, 16-42.
[4] Boris, J.P., Book D.L. (1973) Flux corrected transport. I. SHASTA, a fluid transport algorithm that works. J. Comput. Phys., 11, 38-69.
[5] Zalesak, S.T. (1979) Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., 31, 335-362.
[6] Nagarajan, S., Lele, S., Ferziger, J.H. (2003) A robust high-order compact method for large eddy simulation. J. Comput. Phys., 191, 392-419.
[7] Rizzetta, D.P., Visbal, M.R., Morgan, P.E. (2008) A high-order com-pact finite-difference scheme for large-eddy simulation of active flow control. Prog. Aerosp. Sci., 44, 397-426.
[8] Jiang, G.-S., Shu, C.-W. (1996) Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126, 202-228.
[9] Guo-Hua, T., Xiang-Jiang, Y. (2007) A characteristic-based shock-capturing scheme for hyperbolic problems. J. Comput. Phys., 225, 2083-2097.
[10] Pirozzoli, S (2002) Conservative-hybrid compact-WENO schemes for shock-turbulence interaction. J. Comput. Phys., 178, 81-117.
[11] Trefethen, L.N. (1982) Group velocity in finite difference schemes. SIAM Rev., 24(2), 113-136.

Sponsors, Associates, and Links

---

• International Journal of Power Engineering and Engineering Thermophysics
  
  
• Numerical Algebra and Scientific Computing
  
  
• Transactions on Particle and Nuclear Physics
  
  
• Journal of Probability and Mathematical Statistics
  
  
• Multibody Systems, Nonlinear Dynamics and Control
  
  
• Complex Analysis and Geometry
  
  
• Dynamical Systems and Differential Equations
  
  
• Acoustics, Optics and Radio Physics
  
  
• Progress in Atomic and Molecular Physics
  
  
• Transactions on Condensed Matter Physics
  
  
• Transactions on Computational and Applied Mathematics
  
  
• Progress in Plasma Physics
  
  
• Combinatorics and Graph Theory
  
  
• Research and Practice of Mathematics & Statistics
  
  
• Nuclear Techniques and Applications
  
  
• Journal of Photonics Research
  
  
• Journal of Compressors and Refrigeration
  
  
• Journal of Theoretical Physics Frontiers
  
  
• Journal of Nonlinear Science and Complexity
  
  
• Vacuum Science Journal
  
  
• Computational Fluid Dynamics