Performance Comparison and Analysis of Different Schemes and Limiters
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62491", author = "Wang Wen-long and Li Hua and Pan Sha", title = "Performance Comparison and Analysis of Different Schemes and Limiters", 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.", volume = "5", number = "7", pages = "1057-6", }
