Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy

Journal of Computational Physics

Volumn 160, Issue 2, 2000, Pages 405-452

  Balsara, Dinshaw S ^a   Shu, Chi Wang ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

Conservation law; Convergence; ENO; Monotonicity preserving; Weighted ENO

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL FLUID DYNAMICS; MAGNETOHYDRODYNAMICS; NUMERICAL METHODS;

CONSERVATION LAW; CONVERGENCE; ENO; ESSENTIALLY NON-OSCILLATORY SCHEMES; HIGH-ORDER; HIGHER-ORDER; LOW ORDER; MONOTONICITY; MONOTONICITY PRESERVING; WEIGHTED ENO;

LARGE EDDY SIMULATION;

EID: 0000897959     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6443     Document Type: Article

References (51)

1. Balsara D. S. Linearized formulation of the Riemann problem for adiabatic and isothermal magnetohydrodynamics. Ap. J. Supp. 116:1998;119.
2. Balsara D. S. Total variation diminishing algorithim for adiabatic and isothermal magnetohydrodynamics. Ap. J. Supp. 116:1998;133.
3. D. S. Balsara, TVD scheme for relativistic MHD, submitted for publication.
4. Balsara D. S., Spicer D. A staggered mesh algorithm using higher order Godunov fluxes to ensure solenoidal magnetic fields in MHD simulations. J. Comput. Phys. 149:1997;270.
5. D. S. Balsara, A. Pouquet, D. Ward-Thompson, and, R. M. Crutcher, Numerical MHD studies of turbulence and star formation, in, Interstellar Turbulence, edited by, J. Franco and A. Caraminana, Cambridge Univ. Press, Cambridge, UK, 1998.
6. Brio M., Wu C. C. An upwind differencing scheme for the equations of MHD. J. Comput. Phys. 75:1988;400.
7. Browning G. L., Kreiss H.-O. Comparison of numerical methods for the calculation of two dimensional turbulence. Math. Comput. 52:1989;369.
8. Berger M., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82:1990;64.
9. Casper J. Finite-volume implementation of high-order essentially nonoscillatory schemes in two dimensions. AIAA J. 30:1992;2829.
10. Casper J., Shu C.-W., Atkins H. Comparison of two formulations of high-order accurate essentially nonoscillatory schemes. AIAA J. 32:1994;1970.
11. S. R. Chakravarthy, and, S. Osher, Very High Order Accurate TVD Schemes, AIAA Paper # 85-0363.
12. Cockburn B., Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws. V. Multidimensional systems. J. Comput. Phys. 141:1998;199.
13. Colella P., Woodward P. R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54:1984;174.
14. R. Fedkiw, R. Aslam, T. Merriman, and, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows, submitted for publication.
15. Ghosal S. An analysis of the numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125:1996;187.
16. Godunov S. K. Mat. Sb. 47:1959;357.
17. Harten A. The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws. Comm. Pure Appl. Math. 30:1977;611.
18. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357.
19. Harten A. ENO schemes with subcell resolution. J. Comput. Phys. 83:1989;148.
20. Harten A., Engquist B., Osher S., Chakravarthy S. J. Uniformly high order essentially non-oscillatory schemes, III. J. Comput. Phys. 71:1987;231.
21. W. D. Henshaw, H.-O. Kreiss, and, L. G. Reyna, ICASE Report #88-8, 1988.
22. S. Jamme, F. Torres, and, J. B. Cazalbou, AIAA Paper 97-2070, 1997.
23. Jiang G.-S., Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126:1996;202.
24. Lax P. D. Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7:1954;159.
25. Leonard B. P., Lock A. P., MacVean M. K. The NIRVANA scheme applied to one-dimensional advection. Int. J. Num. Meth. Heat Fluid Flow. 5:1995;341.
26. Lesieur M., Comte P. Large eddy simulations of compressible turbulent flows. Cours AGARD-VKI, Turbulence in Compressible Flows. 1997.
27. Liu X.-D., Osher S., Chan T. Weighted essentially nonoscillatory schemes. J. Comput. Phys. 115:1994;200.
28. Meadows K. R., Kumar A., Hussaini M. Y. A Computational Study of the Interaction between a Vortex and a Shock Wave. 1989.
29. S. P. Pao, and, M. D. Salas, AIAA Paper 81-1205, 1981.
30. Porter D. H., Woodward P. R., Pouquet A. Inertial range structures in decaying compressible trubulence flows. Phys. Fluids. 10:1998;237.
31. Quirk J. A contribution of the great Riemann solver debate. Int. J. Numer. Meth. Fluids. 18:1994;555.
32. Rogerson A., Meiberg E. A numerical study of the convergence properties of ENO schemes. J. Sci. Comput. 5:1990;151.
33. Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
34. P. L. Roe, Some contributions to the modelling of discontinuous flows, in, Lect. in Appl. Math. edited by, B. Engquist, S. Osher, R. J. Somerville, Amer. Math. Soc, 1985, Vol, 22.
35. Roe P. R. Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. J. Comput. Phys. 63:1988;458.
36. Roe P. L., Balsara D. S. Notes on the eigensystem of magnetohydrodynamics. SIAM J. Num. Anal. 56:1996;57.
37. Ryu D., Jones T. Numerical MHD in astrophysics: algorithm and tests for one-dimensional Flow. Ap. J. 442:1995;228.
38. Shu C.-W., Osher S. J. Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77:1988;439.
39. Shu C.-W., Osher S. J. Efficient implementation of essentially non-oscillatory shock capturing schemes II. J. Comput. Phys. 83:1989;32.
40. Shu C.-W. Numerical experiments on the accuracy of ENO and modified ENO schemes. J. Sci. Comput. 5:1990;127.
41. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, edited by, B. Cockburn, C. Johnson, C.-W. Shu, and E. Tadmor (Editor-in-Chief: A. Quarteroni), Springer, 1998, p, 325. [Lecture Notes in Mathematics, Vol, 1697.].
42. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, edited by, B. Cockburn, C. Johnson, C.-W. Shu, and E. Tadmor (Editor-in-Chief: A. Quarteroni), Springer, 1998, p, 325. [Lecture Notes in Mathematics, Vol, 1697.].
43. Shu C.-W., Zang T. A., Erlebacher G., Whitaker D., Osher S. High order ENO schemes applied to two- and three-dimensional compressible Flow. Appl. Numer. Math. 9:1992;45.
44. Sod G. A. A survey of finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27:1978;1.
45. Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5:1968;506.
46. Suresh A., Huynh H. T. Accurate monotonicity preserving scheme with Runge-kutta time-stepping. J. Comput. Phys. 136:1997;83.
47. Sweby P. K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Num. Anal. 21:1984;995.
48. Tadmor E. Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43:1984;369.
49. vanLeer B. Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method. J. Comput. Phys. 32:1979;101.
50. Woodward P., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:1984;115.
51. Yang H. An artificial compression method for ENO schemes, the slope modification method. J. Comput. Phys. 89:1990;125.