Performance Comparison and Analysis of Different Schemes and Limiters

Authors: Wang Wen-long, Li Hua, Pan Sha

Abstract:

Eight difference schemes and five limiters are applied to numerical computation of Riemann problem. The resolution of discontinuities of each scheme produced is compared. Numerical dissipation and its estimation are discussed. The result shows that the numerical dissipation of each scheme is vital to improve scheme-s accuracy and stability. MUSCL methodology is an effective approach to increase computational efficiency and resolution. Limiter should be selected appropriately by balancing compressive and diffusive performance.

Keywords: Scheme; Limiter, Numerical simulation, Riemannproblem.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081197

References:

[1] E. F. Toro, Riemann Solver sand Numerical Methods for Fluid Dynamics. Berlin Heidelberg: Springer- Verlag, 2009,ch.2-4
[2] R W. MacCormack, "The Effect of Viscosity in Hypervelocity Impact Cratering", AIAA paper 1969-354.
[3] A, Jameson W, Schmidt E. Turkel, "Numerical Simulations of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes", AIAA paper 1981-1259.
[4] C. Yan, Computational Fluid Dynamics Method and Application, Beijing: BUAA press, 2006,6.
[5] B. VanLeer, "Flux Vector Splitting for Euler Equations". Lecture Notes in Physics, 1982-70
[6] J L, Steger R F. Warming, "Flux Vector Splitting of the Inviscid Gas-Dynamics Equations with Application to Finite Difference Methods", Journal of Computational Physics, 1981-40 (2)
[7] D. X. Fu, Computational Aerodynamics. Beijing: Space Navigation press, 1994-11.
[8] P. L. Roe, "Approximate Riemann solvers, parameter vectors, and difference schemes", Journal of Computational Physics, vol. 135, 1997.
[9] A. Harten, "High Resolution Schemes for Hyperbolic Conservation Laws", Journal of Computational Physics, 1983, 49:357.
[10] H. X. Zhang, "Non Oscillatory Non Free Parameter Dissipation Scheme", Si Chuan: ACTA AERODYNAMICA SINICA, 1988, 6:143.
[11] M. S. Liou, C. J. Steffen, "A new flux splitting scheme", Journal of Computational Physics, vol. 107, 1993.
[12] M. S. Liou, "A further development of the AUSM+ scheme towards robust and accurate solutions for all speeds", AIAA paper 2003-4116, 2003
[13] M. S. Liou, "A sequel to AUSM, Part II: AUSM+-up for all speeds",. Journal of Computational Physics, 2006, 214:137.
[14] K. H. Kim, C. Kim, O. H. Rho, "Methods for the accurate computations of hypersonic flows I. AUSMPW+ Scheme", Journal of Computational Physics, vol. 174, 2001.
[15] K. H. Kim, C. Kim, "Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows Part I: Spatial discretization", Journal of Computational Physics, vol. 208, 2005.