Computation of free surface flows. Part III. Steady supercritical flow using a generalized lagrangian method

References

• Abbott , M. B. 1979 . Computational Hydraulics; elements of the theory of free surface flow , London, England : Pitman Publishing Ltd .
   Google Scholar
• Cunge , J. , Holley , F. M. and Verweij , A. 1984 . Practical Aspects of Computational River Hydraulics , London : Pitman .
   Google Scholar
• Liggett , J. A. 1967 . Computation (Investigation, Education and Application) . J. of the Hydraulic Engineering, ASCE , 93 ( EM2 ) April : 39 – 71 .
   Google Scholar
• Stoker , J. J. 1957 . Water Waves , New York : Interscience Publishers, Wiley and Sons .
   Google Scholar
• Ippen , A. T. , Knapp , R. T. , Dawson , J. H. , Rouse , H. , Bhoota , B. V. and Hsu , E. Y. 1951 . High-Velocity Flow in Open Channels: A Symposium . Transactions, ASCE , 116 : 265 – 400 .
   Google Scholar
• Ippen , A. T. 1951 . Mechanics of Supercritical Flow . Trans. ASCE , 116 : 268 – 295 .
   Google Scholar
• Ippen , AT. and Dawson , J. H. 1951 . Design of Channel Contractions . Trans. ASCE , 116 : 326 – 346 .
   Google Scholar
• Rouse , H. , Bhoota , B. V. and Hsu , E. Y. 1951 . Design of Channel Expansions . Trans. ASCE , 116 : 347 – 363 .
   Google Scholar
• Liggett , J. A. and Vasudev , S. U. 1965 . “ Slope and friction effects in two dimensional, high speed flow ” . In Proc. 11th International Congress IAHR Vol. 1 , 1 – 12 . Leningrad, , USSR paper 1.25
   Google Scholar
• Jimenez , O. F. and Chaudhry , M. H. 1988 . Computation of supercritical free-surface flows . J. Hvdr. Div., ASCE , 114 ( 4 ) : 377 – 395 .
   Web of Science ®Google Scholar
• Loh , C. Y. and Hui , W. H. 1990 . A New Lagrangian Method for Steady Supersonic Flow Computation, Part I, Godunov Scheme . J. Comput. Physics , 89 ( 1 ) : 207 – 240 .
   Web of Science ®Google Scholar
• Hui , W. H. and Loh , C. Y. 1992 . A New Lagrangian Method for Steady Supersonic Flow Computation, Part II, Slip-Line resolution . J. Comput. Physics , 103 : 450 – 464 .
   Web of Science ®Google Scholar
• Hui , W. H. , Zhao , Y. C and Loh , C. Y. . On the New Lagrangian Approach to Solving the Euler Equations . Proc. of the 4th International Symposium on Computational Fluid Dynamics . September 9–12 . Davis, , USA : University of California .
   Google Scholar
• Yang , J. Y. , Chang , S. H. and Hui , W. H. 1993 . A New Lagrangian Method for Steady Supercritical Shallow Water Flow Computation . J. Computer Methods in Applied Mechanics and Engineering , 104 : 266 – 272 .
   Google Scholar
• Yang , J. Y. , Hsu , C. A. and Chang , S. H. 1993 . Computation of Free Surface Flows. Part I. One-Dimensional Dam- Break Flow . J. of Hydraulic Research , 31 ( 1 ) : 19 – 34 .
   Web of Science ®Google Scholar
• Yang , J. Y. and Hsu , C. A. 1993 . Computation of Free Surface Flows. Part II. Two-Dimensional Unsteady Bore Diffraction . J. of Hydraulic Research , 31 ( 3 ) : 403 – 414 .
   Web of Science ®Google Scholar
• Godunov , S. K. 1959 . A Difference Method for the Numerical Calculation of Discontinuous Solutions in Hydrodynamics . Mat. Sbor. , 47 : 271 – 306 .
   Google Scholar
• Van Leer , B. 1979 . Toward the Ultimate Conservative Difference Scheme, V. A Sequel to Godunov's Method . J. Comput. Physics , 32 : 234
   Google Scholar
• Harten , A. and Osher , S. 1987 . Uniformly High-Order Accurate Nonoscillatory Schemes . I, SIAM J. Numerical Analysis , 24 ( 2 ) : 279 – 309 .
   Web of Science ®Google Scholar
• Harten , A. 1983 . High Resolution Schemes for Hyperbolic Conservation Laws . J. Comput. Physics , 49 : 357 – 393 .
   Web of Science ®Google Scholar